Question

The line segment AB is dilated with the center of dilation at the origin to obtain a line segment A'B'. The coordinates are A(2,4) and A’ (4,8). If the coordinates of B are (x,y), what are the coordinates of B'?

A. (2x, 2y)
B. (x + 2, 2y)
C. (x + 2y + 2)
D. (2x, y)

Answer 1

The dilation factor from A to A' is 2, and so the coordinates of point B' will be obtained by multiplying both coordinates of point B by 2, resulting in B'(2x, 2y).

Step-by-step explanation:

In this mathematics problem, we are dealing with the concept of dilation in coordinate geometry. Given that A(2,4) dilates to A'(4,8), this indicates a dilation factor of 2, because each coordinate of A has been multiplied by 2 to obtain the coordinates of A'. To determine the coordinates of B' when B has coordinates of (x,y), we apply the same dilation factor. The x-coordinate and y-coordinate of B' would then both be multiplied by the dilation factor.

Therefore, the coordinates of B' are (2x, 2y). This corresponds to option A in the provided choices.