Question

Given a scale factor of 2, find the coordinates for the dilation of the line segment with endpoints (–1, 2) and (3, –3)

Answer 1

let the given points be A(-1,2) and B(3,-3)
So the midpoint of AB is M(1,-1/2)
Extend AB to P so that MP = AB
and extend BA to Q so that MQ = AB
it is easy to see that PQ = 2AB

to find P, consider B to be the midpoint of BP
for the x and y of P:
(x+1)/2 = 3 and (y-1/2)/2 = -3
x+1 = 6 and y-1/2 = -6
x = 5 and y = -11/2

P is (5,-11/2) or (5, -5.5)

in the same way ...
Q is (-3 , 9/2) or (-3, 4.5)

check:
AB = √(4^2 + (-5)^2) = √41
PQ = √( 8^2 + 10^2) = √164 = 2√41
so PQ = 2AB and also A,B,P, and Q are collinear