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.
To find the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:
(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.
For point A(1, 2), the new coordinates A' would be:
(x', y') = (5 * 1, 5 * 2) = (5, 10)
For point B(-2, -1), the new coordinates B' would be:
(x', y') = (5 * -2, 5 * -1) = (-10, -5)
Therefore, the coordinates of A' are (5, 10) and the coordinates of B' are (-10, -5).