CAIE IGCSE Mathematics Extended perpendicular lines and bisectors

Practise finding perpendicular gradients, then using points or midpoints to write equations of lines and bisectors in y=mx+c form.

Exam points

calculate the original gradient, then use the negative reciprocal for the perpendicular line
substitute a given point or midpoint into y=mx+c to find c
draw a ruled perpendicular line on a grid when the equation or reference line is given

A is the point (1,5) and B is the point (3,9). M is the midpoint of AB.

Find the equation of the line that is perpendicular to AB and passes through M. Give your answer in the form y=m x+c.

$y=-\frac{1}{2}x+8$
oe

Correct equivalent in different form scores 3.
M1 for gradient of $AB=\frac{9-5}{3-1}$ , $\frac{4}{2}$ , or 2
M1dep for gradient $p=-\frac{1}{\text{their grad of }AB}$
M1dep for substitution of their midpoint into $y=(\text{their }p)x+c$ oe, where their $p\ne0$

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E3.7.1 Find the gradient and equation of a straight line perpendicular to a question 1