Gr 11 Math Ch 4: Perpendicular Lines

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What is the condition for two lines to be perpendicular?

m_1 - m_2 = 1

m_1 ÷ m_2 = 1

m_1 + m_2 = 0

m_1 × m_2 = -1 (correct)

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

Calculate the perpendicular gradient

Use the point-slope form

Simplify the equation

Identify the gradient of the given line (correct)

What is the formula to find the gradient of a perpendicular line?

m_1 = -1/m_2 (correct)

m_1 = m_2

m_1 = -m_2

m_1 = 1/m_2

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

To use the coordinates of the given point Signup and view all the answers

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

Simplify the equation to the standard form Signup and view all the answers

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

To directly read off the gradient Signup and view all the answers

What is the product of the gradients of two perpendicular lines?

-1 Signup and view all the answers

What is the purpose of identifying the gradient of the given line in finding the equation of a perpendicular line?

To find the gradient of the perpendicular line Signup and view all the answers

What form of the equation of a line is required to easily identify the gradient?

Gradient-intercept form Signup and view all the answers

What is the procedure to find the equation of a line that is perpendicular to a given line and passes through a specific point?

Use the point-slope form to find the gradient, then simplify to standard form Signup and view all the answers

If two lines are perpendicular, what can be said about their gradients?

They multiply to -1 Signup and view all the answers

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

m1 × m2 = -1 Signup and view all the answers

What is the implication of the product of the gradients of two lines being -1?

The lines are perpendicular Signup and view all the answers

What is the purpose of calculating the perpendicular gradient using the formula $m_1 = -\frac{1}{m_2}$?

To find the gradient of the perpendicular line Signup and view all the answers

What is the advantage of using the point-slope form of the equation of a line in finding the equation of a perpendicular line?

It is easier to use with the given point and perpendicular gradient Signup and view all the answers

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

It allows the gradient to be easily identified Signup and view all the answers

What is the result of multiplying the gradients of two perpendicular lines?

A value of -1 Signup and view all the answers

What is the relationship between the gradients of two lines if their product is not -1?

The lines are not perpendicular Signup and view all the answers

Gr 11 Math Ch 4: Perpendicular Lines

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