Question

29
the coordinates of the vertices
of a rectangle are (3, 5), (3, 9), (11, 9),
and (11, 5). the rectangle is dilated with
a scale factor of 4 using the origin as
the center of dilation. which one of the
following could not be the coordinates
of a vertex of the dilated rectangle?
a (12, 20)
c (44, 36)
b (44, 12)
d (12, 36)

Explanation:

Step1: Dilate each vertex by scale 4

To dilate a point $(x,y)$ with scale factor $k$ from the origin, use $(k \times x, k \times y)$.

• For $(3,5)$: $(4 \times 3, 4 \times 5) = (12,20)$
• For $(3,9)$: $(4 \times 3, 4 \times 9) = (12,36)$
• For $(11,9)$: $(4 \times 11, 4 \times 9) = (44,36)$
• For $(11,5)$: $(4 \times 11, 4 \times 5) = (44,20)$

Step2: Compare to given options

Match the dilated coordinates with the choices provided.

Answer:

B. (44, 12)