Paper 22 Q15(c)IGCSE 0580 May/June 2023

Question

C is the point (5,-1) and D is the point (13, 15). Find the equation of the perpendicular bisector of CD Give your answer in the form y=mx+c.

This question tests your ability to find the equation of a perpendicular bisector, which requires finding the midpoint of a line segment and the gradient perpendicular to it. This skill is essential for coordinate geometry and appears frequently in IGCSE exams.

Step-by-Step Solution

Key Takeaway

The perpendicular bisector passes through the midpoint of a line segment and has a gradient that is the negative reciprocal of the original line's gradient.

Common Mistakes

Finding the gradient of the perpendicular line as 2 instead of -1/2 - remember it must be the negative reciprocal
Using one of the original points (5, -1) or (13, 15) instead of the midpoint (9, 7) when finding the equation
Making arithmetic errors when calculating the midpoint, particularly with the negative coordinate: (-1 + 15)/2 = 14/2 = 7

Exam Tip

Always check your perpendicular gradient by multiplying it with the original gradient - the result should equal -1 if you've done it correctly.

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