Line AB contains point A(1, 2) and point B(-2, -1). find the coordinates of A' and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin.
a A'(5, 10) and B'(-2, -1)
b A'(5, 10) and B'(-10, -5)
c A'(1, 2) and B'(-10, -5)
d A'(5, 10) and B'(10, 5)
To find the coordinates of A' and B' after a dilation with a scale factor of 5 with the center point of dilation at the origin, we can use the formula for dilation:
(x', y') = (k * x, k * y)
where (x, y) are the original coordinates, (x', y') are the new coordinates after dilation, and k is the scale factor.
Let's apply this formula to the given points:
For point A(1, 2):
x' = 5 * 1 = 5
y' = 5 * 2 = 10
Therefore, A' has the coordinates (5, 10).
For point B(-2, -1):
x' = 5 * (-2) = -10
y' = 5 * (-1) = -5
Therefore, B' has the coordinates (-10, -5).
Therefore, the correct answer is option b: A'(5, 10) and B'(-10, -5).