2

Question

A (-3,1)
1
D (1,0)
0
x
-6 -5 /-4 -3 -2
-1
0
1
2
-1
B (-5 ,- 1)
-2
C (-1 ,- 2)
-3
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

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

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

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

(−1,2)

Answer 1

To find the corresponding ordered pair for point \( A \) when the parallelogram \( ABCD \) is dilated by a magnitude of 2 with a center of dilation at \( (-2, -1) \), we can use the formula for dilation.

The formula for the coordinates of a point \( (x, y) \) after dilation around a center \( (x_c, y_c) \) by a scale factor of \( k \) is:

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

For point \( A(-3, 1) \):

1. The center of dilation is \( (-2, -1) \).
2. The scale factor \( k = 2 \).

Now let's calculate the new coordinates:

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

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

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

The answer is:

\[ \boxed{(-4, 3)} \]