Question

Parallelogram JKLM has the coordinates J(0 , 4), K(9 , 4), L(8 , -1), and M(-1 , -1). Which of the following sets of points represents a dilation from the origin of parallelogram JKLM?
A.
J'(0 , 4), K'(36 , 4), L'(32 , -1), M'(-4 , -1)
B.
J'(0 , 16), K'(36 , 16), L'(32 , -4), M'(-4 , -4)
C.
J'(4 , 8), K'(13 , 8), L'(12 , 3), M'(3 , 3)
D.
J'(0 , 16), K'(36 , 4), L'(32 , -1), M'(-1 , -4)

Answer 1

Dilation from the origin multiplies both coordinates of every vertex by the same scale factor k. From J(0,4) to J' the y-coordinate becomes 4k.

In B, J'(0,16) gives 4k = 16 so k = 4. Applying k = 4 to the other vertices:
- K(9,4) -> (9·4, 4·4) = (36,16)
- L(8,-1) -> (8·4, -1·4) = (32,-4)
- M(-1,-1) -> (-1·4, -1·4) = (-4,-4)

These match option B, so B is correct.