Line A 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 and a center point of dilation at the origin, we can multiply the coordinates of each point by the scale factor.
For point A(-4,1), the coordinates of A' can be found by multiplying each coordinate by 2:
(2 * -4, 2 * 1)
(-8, 2)
For point B(-1,3), the coordinates of B' can be found by multiplying each coordinate by 2:
(2 * -1, 2 * 3)
(-2, 6)
Therefore, the coordinates of A' are (-8, 2) and the coordinates of B' are (-2, 6).
To find the coordinates of a point after a dilation, we need to multiply the coordinates of the original point by the scale factor. Since the center of dilation is at the origin (0,0), we can simply multiply the x-coordinate and the y-coordinate of each point by the scale factor.
Given that the scale factor is 2, we can find the coordinates of A' using the formula:
A'(x', y') = (2 * x, 2 * y)
Let's apply this formula to find the coordinates of A' and B':
For point A(-4,1):
A' = (2 * -4, 2 * 1)
= (-8, 2)
For point B(-1,3):
B' = (2 * -1, 2 * 3)
= (-2, 6)
Therefore, the coordinates of A' after the dilation are (-8, 2) and the coordinates of B' after the dilation are (-2, 6).