Question

Use the image to answer the question y A (-3,1) 2- 1- D (1,0) 1 2 -0+ 0 -1 -2 -6 -5 -4 -3 -1 B (-5,-1) C (-1,-2) -2- -3- < 4 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) Ο (-4, 3) Ο (-5,0) (-1,2) Ο (-3,0)

Answer 1

To find the coordinates of point A after dilation, we can use the formula for dilation:

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

where \( (x_c, y_c) \) is the center of dilation, \( k \) is the magnitude of dilation, and \( (x, y) \) are the original coordinates.

In this case:

- Point A has original coordinates \((-3, 1)\)
- The center of dilation is \((-2, -1)\)
- The magnitude of dilation is \( k = 2\)

Now we can calculate the new coordinates:

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

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

The correct answer is:
\[
(-4, 3)
\]