Question

the line through A(-2,3)and(4,b)is perpendicular to the line 2x-4y=5.find the value of b

Answer 1

A(-2,3),C=(4,b)
we need to find the slope of the line 2x-4y-5=0
a=2
b=-4
slope=$\frac{-a}{b}$=-2/-4= 1/2
this line is perpendicular to  ac
so it's slope is -ve inverse of 1/2=-2

slope of ac=-2
-2=[tex] \frac{y2-y}{x2-x} \\ \\[tex] \frac{b-3}{4--2} =-2 \\ \\ \frac{b-3}{6} = -2 \\ \ b-3=-12 b=-9[/tex]
b=-9

Answer 2

When two lines are perpendicular m1 * m2 = -1
m1 = slope of (-2,3) and (4,b)
m1 = y2-y1/x2-x1
=b-3/4+2
=b-3/6

m2=slope of 2x-4y = 5
m2 = -a/b
= - 2/-4
= 1/2

m1m2=-1
b-3/6 * 1/2 -1
b-3/12 = -1
b-3 = -12
b = -12+3 
b = -9