Asked by HOLAMOM
Given a scale factor of 2, find the coordinates for the dilation of the line segment with endpoints (–1, 2) and (3, –3)
Answers
Answered by
Reiny
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
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