Gr 11 Math Ch 4 SUM: Analytical Geometry
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Questions and Answers

What is the relationship between the gradient of a line and its inclination?

  • The gradient is equal to the cosine of the inclination.
  • The gradient is equal to the sine of the inclination.
  • The gradient is equal to the cotangent of the inclination.
  • The gradient is equal to the tangent of the inclination. (correct)

    • What is the inclination of a vertical line?

  • 180°
  • 0°
  • 90° (correct)
  • Undefined

    • What is the gradient of a horizontal line?

  • infinity
  • 1
  • undefined
  • 0 (correct)

    • If a line has a negative gradient, what can be said about its inclination?

    <p>The inclination is obtuse.</p> Signup and view all the answers

    What is the equation form used when given a gradient and a point?

    <p>Gradient-Point Form</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

    <p>m1 = m2</p> Signup and view all the answers

    What is the relationship between the gradients of two perpendicular lines?

    <p>Their product is -1</p> Signup and view all the answers

    Which form of a line's equation allows us to easily read off the gradient?

    <p>Gradient-intercept form</p> Signup and view all the answers

    What is the first step in finding the equation of a parallel line?

    <p>Identify the gradient of the given line.</p> Signup and view all the answers

    What is the formula for the two-point form of a straight line equation?

    <p>(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    What is the first step in finding the equation of a line perpendicular to a given line?

    <p>Identify the gradient of the given line</p> Signup and view all the answers

    What is the formula for the gradient-point form of a straight line equation?

    <p>y - y1 = m(x - x1)</p> Signup and view all the answers

    What is the purpose of the point-slope form in finding the equation of a parallel line?

    <p>To use the coordinates of the given point.</p> Signup and view all the answers

    What is the formula for finding the gradient of a perpendicular line?

    <p>m_1 = -1/m_2</p> Signup and view all the answers

    What is the advantage of using the point-slope form?

    <p>It can be used to find the equation of a line when given a point and a gradient.</p> Signup and view all the answers

    What is the formula for the gradient-intercept form of a straight line equation?

    <p>y = mx + c</p> Signup and view all the answers

    What is the trigonometric relationship between the gradient and inclination of a line?

    <p>tan(θ) = m</p> Signup and view all the answers

    What is the significance of the constant c in the gradient-intercept form of a straight line equation?

    <p>It represents the y-intercept of the line</p> Signup and view all the answers

    What is the purpose of using the point-slope form of a line's equation?

    <p>To find the equation of a line passing through a specific point</p> Signup and view all the answers

    Why is it important to simplify the equation of a perpendicular line?

    <p>To put the equation in the standard form y = mx + c</p> Signup and view all the answers

    When is the two-point form of a straight line equation used?

    <p>When two points on the line are known</p> Signup and view all the answers

    What is the process of finding the equation of a straight line given two points on the line?

    <p>Use the two-point form to find the equation of the line</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

    <p>They have the same gradient but different y-intercepts</p> Signup and view all the answers

    What is the relationship between the gradient-point form and the two-point form of a straight line equation?

    <p>The gradient-point form is derived from the two-point form</p> Signup and view all the answers

    What is the relationship between the y-intercepts of two perpendicular lines?

    <p>There is no specific relationship</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form of a straight line equation?

    <p>It is easy to find the y-intercept of the line given its equation</p> Signup and view all the answers

    What is the purpose of the gradient-point form of a straight line equation?

    <p>To find the equation of a line given its gradient and a point on the line</p> Signup and view all the answers

    What can be said about the gradient of a line that passes through two points (2, 3) and (4, 5)?

    <p>The gradient is greater than 1</p> Signup and view all the answers

    What is the value of c in the equation y = mx + c?

    <p>The y-intercept of the line</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form of a straight line equation?

    <p>It is easy to read off the y-intercept</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>Their gradients are negative reciprocals</p> Signup and view all the answers

    What is the equation of the line that passes through the point (3, 4) and has a gradient of 2?

    <p>y = 2x + 2</p> Signup and view all the answers

    What can be said about the graph of a line with a gradient of 0?

    <p>It is a horizontal line</p> Signup and view all the answers

    What is the equation of the line that passes through the points (2, 3) and (4, 5)?

    <p>y = x + 1</p> Signup and view all the answers

    What is the value of θ for a horizontal line?

    <p>0°</p> Signup and view all the answers

    If a line has a gradient of 2, what is the value of tan(θ)?

    <p>2</p> Signup and view all the answers

    What is the equation form used when given a gradient and the y-intercept?

    <p>Gradient-Intercept Form</p> Signup and view all the answers

    If a line has a negative gradient, what can be said about its inclination?

    <p>The inclination is obtuse</p> Signup and view all the answers

    What is the gradient of a line that is parallel to a line with a gradient of 3?

    <p>3</p> Signup and view all the answers

    What is the formula for finding the equation of a line parallel to a given line and passing through a point?

    <p>y - y1 = m(x - x1)</p> Signup and view all the answers

    What is the significance of the constant c in the gradient-intercept form of a straight line equation?

    <p>It represents the y-intercept of the line</p> Signup and view all the answers

    What is the relationship between the gradient of a line and its inclination?

    <p>m = tan(θ)</p> Signup and view all the answers

    What is the inclination of a line with a gradient of 1?

    <p>45°</p> Signup and view all the answers

    What is the purpose of simplifying the equation of a parallel line?

    <p>To make the equation easier to read and understand</p> Signup and view all the answers

    What is the main advantage of using the gradient-intercept form of a line's equation?

    <p>It allows us to easily read off the gradient and y-intercept.</p> Signup and view all the answers

    What is the first step in finding the equation of a line perpendicular to a given line?

    <p>Identify the gradient of the given line.</p> Signup and view all the answers

    What is the relationship between the gradients of two perpendicular lines?

    <p>They multiply to -1.</p> Signup and view all the answers

    What is the purpose of the point-slope form of a line's equation?

    <p>To find the equation of a line given a point and a gradient.</p> Signup and view all the answers

    Why is it important to ensure the given line's equation is in gradient-intercept form?

    <p>To directly read off the gradient.</p> Signup and view all the answers

    What is the formula for finding the gradient of a perpendicular line?

    <p>m_1 = -1/m_2</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>Their gradients multiply to -1.</p> Signup and view all the answers

    What should be the final step in finding the equation of a perpendicular line?

    <p>Simplify the equation to the standard form.</p> Signup and view all the answers

    What is the value of θ when the gradient of a line is 3/4?

    <p>53.1°</p> Signup and view all the answers

    If a line has a gradient of -2/3, what is the value of θ?

    <p>210°</p> Signup and view all the answers

    What is the equation of a line that is parallel to y = 2x + 3 and passes through (1, 4)?

    <p>y = 2x - 1</p> Signup and view all the answers

    What is the relationship between the gradients of two parallel lines?

    <p>m₁ = m₂</p> Signup and view all the answers

    What is the inclination of a line with a gradient of 1/2?

    <p>26.6°</p> Signup and view all the answers

    What is the primary purpose of using the gradient-point form of a straight line equation?

    <p>To derive the equation of a line given the gradient and a point on the line</p> Signup and view all the answers

    What is the relationship between the gradient of a line and the constant c in the gradient-intercept form?

    <p>The constant c is the y-intercept of the line, and the gradient is the slope</p> Signup and view all the answers

    What is the equation of a line that is parallel to y = 3x - 2 and passes through (2, 5)?

    <p>y = 3x + 3</p> Signup and view all the answers

    Given two points (x1, y1) and (x2, y2) on a line, what is the first step in deriving the equation of the line in gradient-intercept form?

    <p>Find the gradient using the formula m = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    What is the value of θ when the gradient of a line is -1/3?

    <p>210°</p> Signup and view all the answers

    What is the equation of a line that is parallel to y = 2x + 1 and passes through (3, 7)?

    <p>y = 2x + 3</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form of a straight line equation over the two-point form?

    <p>It is easier to find the y-intercept</p> Signup and view all the answers

    What is the relationship between the two-point form and the gradient-point form of a straight line equation?

    <p>They are equivalent forms of the same equation</p> Signup and view all the answers

    What is the relationship between the gradient of a line and its inclination?

    <p>m = tan(θ)</p> Signup and view all the answers

    What is the value of θ when the gradient of a line is 2/5?

    <p>37.7°</p> Signup and view all the answers

    Given a line with a gradient of m and a point (x1, y1) on the line, what is the equation of the line in gradient-point form?

    <p>y - y1 = m(x - x1)</p> Signup and view all the answers

    What is the significance of the constant c in the gradient-intercept form of a straight line equation?

    <p>It is the y-intercept of the line</p> Signup and view all the answers

    What is the primary application of the two-point form of a straight line equation?

    <p>To find the equation of a line given two points</p> Signup and view all the answers

    What is the gradient of a line perpendicular to a line with a gradient of 3/4?

    <p>-4/3</p> Signup and view all the answers

    If a line has a gradient of 2 and passes through the point (3, 4), what is its equation in the gradient-intercept form?

    <p>y = 2x + 1</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>They have gradients that multiply to -1</p> Signup and view all the answers

    If a line passes through the points (2, 3) and (4, 5), what is its gradient?

    <p>1/1</p> Signup and view all the answers

    What is the equation of a line perpendicular to a line with equation y = 2x + 1 and passing through the point (3, 4)?

    <p>y = -1/2x + 6</p> Signup and view all the answers

    What is the gradient of a line parallel to a line with a gradient of 2/3?

    <p>2/3</p> Signup and view all the answers

    If a line has a gradient of -1 and passes through the point (2, 3), what is its equation in the gradient-intercept form?

    <p>y = -1x + 5</p> Signup and view all the answers

    What is the equation of a line perpendicular to a line with equation y = x + 2 and passing through the point (1, 3)?

    <p>y = -1x + 4</p> Signup and view all the answers

    If a line passes through the points (2,3) and (4,5), what is the value of m in the equation y=mx+c?

    <p>3/2</p> Signup and view all the answers

    What is the equation of a line that passes through the point (3,4) and is parallel to the line y=2x+1?

    <p>y=2x+2</p> Signup and view all the answers

    If a line has an inclination of 30°, what is the value of m in the equation y=mx+c?

    <p>tan(30°)</p> Signup and view all the answers

    What is the equation of a line that is perpendicular to the line y=3x-2 and passes through the point (1,1)?

    <p>y=-x/3+4/3</p> Signup and view all the answers

    What is the value of c in the equation y=2x+c if the line passes through the point (2,5)?

    <p>3</p> Signup and view all the answers

    If a line has a gradient of -1, what can be said about its inclination?

    <p>It is 135°</p> Signup and view all the answers

    What is the equation of a line that passes through the points (3,2) and (5,4)?

    <p>y=x-1</p> Signup and view all the answers

    If a line has a gradient of 3, what is the gradient of a line perpendicular to it?

    <p>-1/3</p> Signup and view all the answers

    What is the equation of a line that is perpendicular to the line y = 2x + 3 and passes through the point (1, 4)?

    <p>y = -1/2x + 5</p> Signup and view all the answers

    What is the purpose of the gradient-intercept form of a straight line equation?

    <p>To easily read off the gradient and y-intercept</p> Signup and view all the answers

    If two lines have gradients of 2 and -1/2, are they perpendicular?

    <p>Yes, because their gradients multiply to -1</p> Signup and view all the answers

    What is the gradient of a line that is parallel to the line y = 3x - 2?

    <p>3</p> Signup and view all the answers

    What is the equation of a line that is perpendicular to the line y = x - 2 and passes through the point (2, 3)?

    <p>y = -x + 4</p> Signup and view all the answers

    If two lines have gradients of -2 and 1/2, are they perpendicular?

    <p>No, because their gradients do not multiply to -1</p> Signup and view all the answers

    What is the equation of a line that is parallel to the line y = -x + 3 and passes through the point (1, 2)?

    <p>y = -x + 2</p> Signup and view all the answers

    If a line has a gradient of 1/2, what is the gradient of a line that is perpendicular to it?

    <p>2</p> Signup and view all the answers

    If a line has a gradient of -2, what is the value of θ?

    <p>135°</p> Signup and view all the answers

    A line passes through the points (2, 3) and (4, 5). What is the value of the gradient?

    <p>3/2</p> Signup and view all the answers

    What is the equation of a line that is parallel to the line y = 2x + 3 and passes through the point (1, 4)?

    <p>y = 2x + 2</p> Signup and view all the answers

    If two lines have gradients of 3 and -3, what can be said about the lines?

    <p>They are perpendicular</p> Signup and view all the answers

    What is the value of tan(θ) for a line with a gradient of 1/2?

    <p>1/2</p> Signup and view all the answers

    What is the equation form used when given a gradient and a point on the line?

    <p>Point-Slope Form</p> Signup and view all the answers

    If a line has a gradient of 4, what is the value of θ?

    <p>76°</p> Signup and view all the answers

    What is the equation of a line that is perpendicular to the line y = 3x - 2 and passes through the point (2, 1)?

    <p>y = -1/3x + 3</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

    <p>They have the same gradient but different y-intercepts</p> Signup and view all the answers

    A line has a gradient of -3/2 and passes through the point (2, 3). What is the equation of the line?

    <p>y = -3/2x - 1</p> Signup and view all the answers

    What is the main purpose of ensuring the given line's equation is in gradient-intercept form?

    <p>To directly read off the gradient</p> Signup and view all the answers

    Two lines have gradients of 2 and 1/2. What can be said about these lines?

    <p>They are perpendicular</p> Signup and view all the answers

    What is the first step in finding the equation of a line perpendicular to a given line?

    <p>Calculate the perpendicular gradient</p> Signup and view all the answers

    What is the purpose of the point-slope form of a line's equation in finding the equation of a perpendicular line?

    <p>To use the coordinates of the given point and the perpendicular gradient</p> Signup and view all the answers

    If two lines are perpendicular, what is true about their y-intercepts?

    <p>They are different</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form of a line's equation?

    <p>It allows for easy identification of the gradient</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>Their gradients multiply to -1</p> Signup and view all the answers

    What is the last step in finding the equation of a perpendicular line?

    <p>Simplify the equation</p> Signup and view all the answers

    What is true about the gradients of two parallel lines?

    <p>They are the same</p> Signup and view all the answers

    What is the purpose of calculating the perpendicular gradient?

    <p>To find the equation of the perpendicular line</p> Signup and view all the answers

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