Point b(5, −2) is translated 4 units right and 2 units down and then dilated by a factor of 2 using the origin as the center of dilation. what is the resultant point?

The resultant point is (18, -8)

Explanation:
1- For transformation:
The original point is (5,-2). The point is translated:
i- 4 units to the right, this means that the value of the x-coordinate increased by 4
ii- 2 units down, this means that the value of the y-coordinate decreased by 2.
Based on this, the translated point would be:
(5+4 , -2-2) which is (9, -4)

2- For dilation:
We are given that the dilation factor is 2, therefore:
dilated x-coordinate = 2 * 9 = 18
dilated y-coordinate = 2 * -4 = -8
Based on the above, the dilated point is (18, -8)

Hope this helps :)