The line AB is shown on the grid. b)Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.

Step-by-step explanation:

a)

first step: find the gradient slope of line AB

A(-1,-2) B(7,2)

gradient=change in y/change in x

M=[2-(-2)]/[7-(-1)

M=4/8

M=1/2

the gradient of the straight line is given by

M1*M2=-1

1/2*M2=-1

multiply both sides by the reciprocal of 1/2

2*1/2*M2=-1*2

M2= -2.

b)

first find the mind point of line AB

A(-1,-2) B(7,2)

M.P=(x1+x2)/2 ,(y+y2)/2

M.P=(-1+7)/2 ,(-2+2)/2

M.P=6/2 ,0/2

M.P=3,0

ALSO THE GRADIENT PERPENDICULAR TO LINE AB IS;

M= -2

equation of a line perpendicular to AB and passes through the midpoint of AB

Y-Y1=M(X-X1). (3,0). M=-2

y-0=-2(x-3)

y= -2x+6