Rectangle A(0,0)B(6,0)C(6,4)D(0,4) is draw 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.

Answer 1

To find the corresponding ordered pair of point A(0,0) after the dilation with a center at (3,0) and a magnitude of 3, we can follow these steps:

1. Determine the distance from the center of dilation (3, 0) to point A (0, 0):

   • The distance along the x-axis: \( |0 - 3| = 3 \)
   • The distance along the y-axis: \( |0 - 0| = 0 \)

2. Under dilation with a magnitude of 3, we need to multiply the distance from the center by this factor:

   • New distance in the x-direction: \( 3 \times 3 = 9 \)
   • New distance in the y-direction: \( 3 \times 0 = 0 \)

3. Since point A is left of the center (3,0), we move 9 units to the left from the center:

   • New x-coordinate: \( 3 - 9 = -6 \)
   • New y-coordinate remains the same: \( 0 \)

Thus, the new coordinates of point A after dilation will be \((-6, 0)\).

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