A -3,1 B -5,-1 C -1,-2 D 1,0

Question

Suppose parallelogram ABCD
is dilated using a magnitude of 2 and a center of dilation at (−2,−1)
. What would be the corresponding ordered pair at point A
?

(1 point)
Responses

(−5,0)
left parenthesis negative 5 comma 0 right parenthesis

(−4,3)
left parenthesis negative 4 comma negative 3 right parenthesis

(−3,0)
left parenthesis negative 3 comma 0 right parenthesis

(−1,2)

Answer 1

To find the corresponding point \( A' \) after dilation, we will use the center of dilation \( (h, k) = (-2, -1) \), the original point \( A(-3, 1) \), and the dilation factor \( m = 2 \).

The formula for the dilation of a point \( (x, y) \) about a point \( (h, k) \) is given by:

\[ (x', y') = (h + m(x - h), k + m(y - k)) \]

Plugging in the values:

• \( h = -2 \)
• \( k = -1 \)
• \( m = 2 \)
• \( A = (-3, 1) \)

We calculate:

1. Calculate \( x' \): \[ x' = -2 + 2(-3 - (-2)) = -2 + 2(-3 + 2) = -2 + 2(-1) = -2 - 2 = -4 \]

2. Calculate \( y' \): \[ y' = -1 + 2(1 - (-1)) = -1 + 2(1 + 1) = -1 + 2(2) = -1 + 4 = 3 \]

So the dilated point \( A' \) is

\[ A' = (-4, 3) \]

Thus, the corresponding ordered pair at point A after dilation is:

Response: (−4, 3)