line AB contains point a -4,1 and point b -1,3. find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin
To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we need to multiply the x and y coordinates of each point by 2.
For point A (-4, 1), the new coordinates A' will be:
x-coordinate of A' = (x-coordinate of A) * (scale factor) = (-4) * 2 = -8
y-coordinate of A' = (y-coordinate of A) * (scale factor) = 1 * 2 = 2
So, the coordinates of A' are (-8, 2).
For point B (-1, 3), the new coordinates B' will be:
x-coordinate of B' = (x-coordinate of B) * (scale factor) = (-1) * 2 = -2
y-coordinate of B' = (y-coordinate of B) * (scale factor) = 3 * 2 = 6
So, the coordinates of B' are (-2, 6).