Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 6 to 2 and its y-axis ranges from negative 3 to 2, both by 1-unit increments. 4 points forming a parallelogram are plotted, labeled upper A (-3,1), upper B (-5,-1), upper C (-1,-2), and upper D (1,0), respectively.

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

(−1,2)
left parenthesis negative 1 comma 2 right parenthesis

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

(−3,0)

Answer 1

To find the coordinates of point A after dilation, we can follow these steps:

1. Identify the original coordinates of point A: \( A(-3, 1) \).
2. The center of dilation is given as \( C(-2, -1) \).
3. The magnitude of dilation is 2.

The formula for dilation from a center point \( C(x_c, y_c) \) is given by:

\[
(x', y') = \left( x_c + k(x - x_c), y_c + k(y - y_c) \right)
\]

where \( k \) is the magnitude of dilation.

Plugging in the values:

- Coordinates of point A: \( (x, y) = (-3, 1) \)
- Center of dilation: \( C(-2, -1) \)
- Magnitude of dilation: \( k = 2 \)

Now, we can apply the formula:

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

2. For the y-coordinate:
\[
y' = -1 + 2(1 - (-1)) = -1 + 2(1 + 1) = -1 + 2 \cdot 2 = -1 + 4 = 3
\]

Thus, the new coordinates of point A after the dilation are \( (-4, 3) \).

Among the given options, the correct response is:

**(−4,3)**