Determine the scale factor used in a dilation of A and B with a center point of dilation at the origin
A'(-6,8) B'(4,-8) A'(-3,4) B'(2,-4)
To find the scale factor, we need to calculate the ratio of the corresponding side lengths of the original and dilated figures.
Let's consider the x-coordinates of the points A and A'.
The original x-coordinate of point A is -6, and after dilation it becomes -3. The change in x-coordinate is -3 - (-6) = 3.
Similarly, the change in x-coordinate for point B is 2 - 4 = -2.
To calculate the scale factor, we divide the change in x-coordinate for A' by the change in x-coordinate for A:
(scale factor) = (change in x-coordinate for A') / (change in x-coordinate for A)
= 3 / 3
= 1
Similarly, let's consider the y-coordinates of the points A and A'.
The original y-coordinate of point A is 8, and after dilation it becomes 4. The change in y-coordinate is 4 - 8 = -4.
Similarly, the change in y-coordinate for point B is -4 - (-8) = 4.
To calculate the scale factor, we divide the change in y-coordinate for A' by the change in y-coordinate for A:
(scale factor) = (change in y-coordinate for A') / (change in y-coordinate for A)
= -4 / -4
= 1
Therefore, the scale factor used in the dilation of A and B with a center point of dilation at the origin is 1.