Question

The parallelogram's vertices are located as follows: upper A at left parenthesis negative 3 comma 1 right parenthesis, upper B at left parenthesis negative 5 comma negative 1 right parenthesis, upper C at left parenthesis negative 1 comma negative 2 right parenthesis, and upper D at left parenthesis 1 comma 0 right parenthesis. Suppose parallelogram ABCD 𝐴 𝐵 𝐶 𝐷 is dilated using a magnitude of 2 and a center of dilation at (−2,−1) ( − 2 , − 1 ) . What would be the corresponding ordered pair at point A 𝐴 ? (1 point) Responses (−3,0) ( − 3 , 0 ) left parenthesis negative 3 comma 0 right parenthesis (−4,3) ( − 4 , 3 ) left parenthesis negative 4 comma negative 3 right parenthesis (−5,0) ( − 5 , 0 ) left parenthesis negative 5 comma 0 right parenthesis (−1,2)

Answer 1

A' = O + 2(A − O) where O = (−2,−1).

A − O = (−3 − (−2), 1 − (−1)) = (−1, 2)
2(A − O) = (−2, 4)
A' = (−2,−1) + (−2,4) = (−4,3)

So the image of A is (−4, 3).