Question

A (0,0)
B (6,0)
C (6,4)
D (0,4)

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?

The new ordered pair would be at (_, _)

Answer 1

To find the new position of point A after dilation, we can use the formula for dilation. The formula for the coordinates of a point \( (x, y) \) after a dilation centered at \( (h, k) \) with a magnitude of \( r \) is given by:

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

In this problem, we have:

- Point A at \( (0, 0) \)
- Center of dilation at \( (3, 0) \)
- Magnitude of dilation \( r = 3 \)

Using the coordinates of point A and the center of dilation, we can substitute into the formula:

1. \( x = 0 \)
2. \( y = 0 \)
3. \( h = 3 \) (x-coordinate of the center)
4. \( k = 0 \) (y-coordinate of the center)
5. \( r = 3 \)

Now we calculate the new coordinates:

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

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

So the new ordered pair for point A after dilation is \( (-6, 0) \).

The final answer is:

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