Questions and Answers
Which lines are perpendicular to the line $y - 1 = (x+2)$? Check all that apply.
Are Trish and Demetri correct in their statements about the parallel line to $y - 3 = −(x + 1)$ that passes through (4, 2)?
What is the slope of the line that is parallel to the given line and passes through the given point?
-1/4
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?
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What is the y-intercept of the line that is parallel to the given line and passes through the given point?
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Which line is parallel to the line $8x + 2y = 12$?
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What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?
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What is the equation of the line that is parallel to the given line and passes through the given point?
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What is the slope of the given line segment with endpoints at (4, -6) and (0, 2)?
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What is the midpoint of the given line segment with endpoints at (4, -6) and (0, 2)?
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What is the slope of the perpendicular bisector of the given line segment?
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What is the equation, in slope-intercept form, of the perpendicular bisector?
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What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)?
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What is the equation of the line parallel to the given line with an x-intercept of 4?
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Which points are on the perpendicular bisector of the given segment? Check all that apply.
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Study Notes
Perpendicular Lines
- A line is perpendicular to another if their slopes are negative reciprocals.
- The line y - 1 = (x + 2) has a slope of 1, thus lines perpendicular to it will have a slope of -1.
- Examples of perpendicular lines include:
- y + 2 = -3(x - 4) (slope -3)
- y = -3x - 5/3 (slope -3)
- 3x + y = 7 (slope -3)
Parallel Lines
- Parallel lines have the same slope.
- For the equation y - 3 = -(x + 1) with slope -1, the parallel line must also have a slope of -1 and pass through (4, 2).
- Correct statement:
- Trish: y - 2 = -1(x - 4) is correct.
- Demetri: y = -x + 6 is incorrect. The correct y-intercept through (4, 2) is 6.
Slope and Equation in Point-Slope Form
- The slope of a parallel line through a given point can be identified.
- Example:
- Given slope of -1/4 leads to the equation: y + 4 = -1/4(x + 2).
- The y-intercept can be derived; for the previous example, it is -9/2.
Criteria for Perpendicular Lines
- For a line to be perpendicular to another while sharing the same y-intercept:
- The slope must be the negative reciprocal of the other line's slope.
- Example: Given slope -3/2 at y-intercept -2.
Line Equations
- A line parallel to a given line and through a point can often be simplified (e.g., y = -4 indicates a horizontal line).
- The equation of a line perpendicular to a specific line passing through a point can be derived; for instance, with (5, 3), it results in 4x - 5y = 5.
Line Segment Properties
- Slope of a line segment is determined using endpoints; for (4, -6) and (0, 2), the slope is -2.
- Midpoint calculation results in (2, -2).
- Slope of the perpendicular bisector is the negative reciprocal of the line segment slope, yielding 1/2. Its equation is Y = (1/2)x - 3.
Points on Perpendicular Bisector
- Identification of points on a perpendicular bisector is key for geometry.
- Points checked may include:
- (−8, 19)
- (1, −8)
- (−5, 10)
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Description
Test your understanding of linear equations in geometry with this quiz focusing on parallel and perpendicular lines. You'll analyze different linear equations to determine which are perpendicular or parallel to given lines. Perfect for geometry students looking to reinforce their knowledge.
