CAIE A-Level Mathematics AS 1.3.2 Line Equation Forms Questions

$k(5-2 x)^{\frac{1}{2}}=-3$
Equating their $\frac{\mathrm{d} y}{\mathrm{~d} x}$ of the form $k(5-2 x)^{\frac{1}{2}}$ to -3 .

[B is ](2,6)
Gradient $A B=m_{1}=\frac{32-6}{-2-2}$,gradient of perpendicular $=-\frac{1}{m_{1}}=\frac{4}{26}$

M1*

For A, y must be 32 .
Clear use of $\frac{\text { difference in y co-ordinates }}{\text { difference in x co-ordinates }}$ for points
A and B, condone inconsistent order, and using
$m_{1} m_{2}=-1$.
If incorrect values or another complete method used, then working must be clear.

Mid point is $\left(\frac{2-2}{2}, \frac{6+32}{2}\right)=(0,19)$

M1*

Finding the midpoint of A B using A and B. If
incorrect values used then all working must be clear.
For A, y must be 32 .

$y-19=\frac{2}{13}(x-0)$
Finding the equation of the perpendicular bisector using their midpoint and their perpendicular
gradient.

2 x-13 y+247=0 or $\pm$ integer multiples of this.