Answer
(4, -24)
Step-by-step explanation
The given directive D₄.rᵧ=₋ₓ means we should dilate the given coordinate by a factor of 4, and the other one means a reflection about the line y = -x
Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates (kx, ky).
(6, -1) dilated by a factor of 4 means k = 4, it becomes
(6, -1) = [(4)(6), (4)(-1)] = (24, -4)
Then, reflecting a coordinate about the line y = -x turns the coordinate (x, y) into (-y, -x)
(24, -4) turns into (4, -24)
Hope this Helps!!!