line segment AB has endpoints A (-6,4) and (-8,2) find the coordinates of A and B after a dilation with a scale factor of 1/2 centered at the origin
To find the coordinates of A and B after the dilation, we can use the formula for dilation centered at the origin:
(x', y') = (kx, ky)
where (x', y') are the new coordinates after dilation, (x, y) are the original coordinates, and k is the scale factor.
For point A (-6, 4), we can plug the values into the formula:
(x', y') = (kx, ky)
(x', y') = (1/2)(-6, 4)
(x', y') = (-3, 2)
So the new coordinates for point A after the dilation are (-3, 2).
Similarly, for point B (-8, 2):
(x', y') = (kx, ky)
(x', y') = (1/2)(-8, 2)
(x', y') = (-4, 1)
So the new coordinates for point B after the dilation are (-4, 1).
Therefore, after the dilation with a scale factor of 1/2 centered at the origin, point A is (-3, 2) and point B is (-4, 1).