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 (one half), centered at the origin.
To perform a dilation with a scale factor of 1/2 centered at the origin, we need to multiply the coordinates of each point by a factor of 1/2.
For point A (-6, 4):
x-coordinate of A' = (1/2)(-6) = -3
y-coordinate of A' = (1/2)(4) = 2
Therefore, the coordinates of A' are (-3, 2).
For point B (-8, 2):
x-coordinate of B' = (1/2)(-8) = -4
y-coordinate of B' = (1/2)(2) = 1
Therefore, the coordinates of B' are (-4, 1).