Line segment AB has endpoints A (−6, 4) and B (−8, 2). Find the coordinates of A′ and B′ after a dilation with a scale factor of 1/2, centered at the origin.
To find the coordinates of A' after the dilation, we need to multiply the coordinates of A by the scale factor of 1/2.
The x-coordinate of A' is obtained by multiplying the x-coordinate of A by 1/2:
x-coordinate of A' = x-coordinate of A * 1/2 = -6 * 1/2 = -3
The y-coordinate of A' is obtained by multiplying the y-coordinate of A by 1/2:
y-coordinate of A' = y-coordinate of A * 1/2 = 4 * 1/2 = 2
So the coordinates of A' are (-3, 2).
Similarly, to find the coordinates of B' after the dilation, we need to multiply the coordinates of B by the scale factor of 1/2.
The x-coordinate of B' is obtained by multiplying the x-coordinate of B by 1/2:
x-coordinate of B' = x-coordinate of B * 1/2 = -8 * 1/2 = -4
The y-coordinate of B' is obtained by multiplying the y-coordinate of B by 1/2:
y-coordinate of B' = y-coordinate of B * 1/2 = 2 * 1/2 = 1
So the coordinates of B' are (-4, 1).
Therefore, A' has coordinates (-3, 2) and B' has coordinates (-4, 1) after the dilation.