Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 6 to 7 and its y-axis ranges from negative 5 to 5, both by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A, (0,0) upper B, (6,0) upper C, (6,4) and upper D, (0,4) respectively.

Rectangle ABCD
is drawn on a coordinate plane. If the rectangle were dilated using a magnitude of 3
and center of dilation at (3,0)
, what would be the corresponding ordered pair to point A
?

(1 point)
The new ordered pair would be at (
,
).

Answer 1

To find the new coordinates of point A (0, 0) after a dilation of magnitude 3 centered at (3, 0), we can use the formula for dilation:

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

Where:
- \((x', y')\) are the coordinates after dilation,
- \((x_c, y_c)\) is the center of dilation,
- \(k\) is the scale factor (dilation magnitude),
- \((x, y)\) are the original coordinates.

For point A:
- Original coordinates \((x, y) = (0, 0)\)
- Center of dilation \((x_c, y_c) = (3, 0)\)
- Magnitude \(k = 3\)

Now we can substitute these values into the formula:

\[
x' = 3 + 3(0 - 3)
\]
\[
x' = 3 + 3(-3)
\]
\[
x' = 3 - 9
\]
\[
x' = -6
\]

Now for the y-coordinate:

\[
y' = 0 + 3(0 - 0)
\]
\[
y' = 0 + 3(0)
\]
\[
y' = 0
\]

Thus, the new ordered pair for point A after the dilation is:

\[
(-6, 0)
\]

So the answer is:

The new ordered pair would be at \((-6, 0)\).