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Exercises for Question Type 2: Finding the equation of a perpendicular bisector given a line segment with a mid point - IB | RevisionDojo

Question 1

Find the equation of the perpendicular bisector of the segment on the line $y = \tfrac{3}{4}x + 2$ with midpoint at $x = 4$ .

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Question 2

Find the equation of the perpendicular bisector of the segment on the line $y = -x - 2$ with midpoint at $x = 0$ .

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Question 3

Find the equation of the perpendicular bisector of the segment on the line $y = 4x - 1$ with midpoint at $x = 2$ .

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Question 4

This question requires students to determine the equation of a line that is perpendicular to a given line and passes through a specific point (the midpoint of a segment on that line). It tests knowledge of coordinates, perpendicular gradients, and the general form of a linear equation.

Find the equation of the perpendicular bisector of a line segment on the line $y = -3x + 5$ which has its midpoint at $x = -1$ . Give your answer in the form $ax + by + c = 0$ , where $a, b, c \in \mathbb{Z}$ .

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Question 5

Find the equation of the perpendicular bisector of the segment on the line $y = 2x + 1$ with midpoint at $x = 3$ .

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Question 6

Find the equation of the perpendicular bisector of the segment on the line $y = 5x + 4$ with midpoint at $x = 3$ .

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Question 7

Find the equation of the perpendicular bisector of the segment on the line $y = -\frac{2}{3}x + 6$ with midpoint at $x = 3$ .

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Question 8

The perpendicular bisector of a line segment is the line that is perpendicular to the segment and passes through its midpoint. To find the equation of a line, the slope and a point on the line are required. For perpendicular lines with slopes $m_1$ and $m_2$ , the relationship is $m_1 \cdot m_2 = -1$ .

Find the equation of the perpendicular bisector of the line segment on the line $y = -5x + 3$ with midpoint at $x = 1$ . Give your answer in the form $ax + by + d = 0$ , where $a, b, d \in \mathbb{Z}$ .

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Question 9

The question tests understanding of coordinate geometry, specifically finding midpoints, perpendicular gradients, and the equation of a line.

Find the equation of the perpendicular bisector of the segment on the line $y = -\frac{1}{4}x$ with midpoint at $x = 4$ .

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Question 10

Find the equation of the perpendicular bisector of the segment on the line $y = \frac{1}{2}x - 4$ with midpoint at $x = 6$ .

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Question 11

Find the equation of the perpendicular bisector of the segment on the line $y = -2x + 9$ with midpoint at $x = -2$ .

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Question 12

Find the equation of the perpendicular bisector of the segment on the line $y = 7x - 7$ with midpoint at $x = 8$ .

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Question Type 2: Finding the equation of a perpendicular bisector given a line segment with a mid point Exercises