CAIE IGCSE Additional Math 7.2 parallel and perpendicular gradients

Use this gradient page to convert a line's gradient into the negative reciprocal, then use a point to find the new line equation.

Exam points

Use the negative reciprocal gradient to write the equation of a perpendicular line.

[Maximum number: 4]

The coordinates of points A and B are (-5,6) and (4,-6) respectively. The point C lies on the line AB, between A and B, such that $\frac{AC}{CB}=\frac12$ .

The line CD is perpendicular to AB. Find the equation of CD in the form y=mx+c.

$m_{AB}=\frac{-6-6}{4-(-5)}=-\frac43$
B1
$m_{CD}=\frac34$
M1
$y-2=\frac34(x+2)$
M1
$y=\frac34x+\frac72$
A1

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7.2. Use parallel and perpendicular gradients question 1