Question

Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 2, centered at the origin where the end points are A ( 3, 7) and B (4, 9).

Answer 1

To find the coordinates of A' and B' after dilation of the line segment AB with a scale factor of 2, centered at the origin, we can use the formula for dilation in the coordinate plane.

The formula for dilation is given by: (x', y') = (kx, ky)

Here, (x, y) are the original coordinates, (x', y') are the new coordinates after dilation, and k is the scale factor.

For point A (3, 7):
x' = 2 * 3 = 6
y' = 2 * 7 = 14

So, A' is located at (6, 14).

For point B (4, 9):
x' = 2 * 4 = 8
y' = 2 * 9 = 18

So, B' is located at (8, 18).

Therefore, A' has coordinates (6, 14) and B' has coordinates (8, 18).