Question

A company is looking to design a new cover for their smartphone. The scale drawing of the design is shown below. The coordinates of the actual cover are: R' (12, 0); S' (0, 0); T' (0, 16); U' (12, 16). Is the design of the cover similar to the actual cover?

Rectangle RSTU is shown. Point R is at 3,0. S is at 0,0. T is at 0,4. U is at 3,4.

Yes; the corresponding sides are proportional.
No; the corresponding sides are not proportional.
Yes; the corresponding angles are proportional.
No; the corresponding angles are not proportional.

Answer 1

The vertices of the current cover are:
R '(12, 0); S '(0, 0); T '(0, 16); U '(12, 16)
The vertices of the design are:
R (3, 0); S (0, 0); T (0, 4); U (3, 4)
We then have the following relationship:
((1/4) x ', ((1/4) y') -----> (x, y)
Equivalently:
(1/4) R '= R
(1/4) S '= S
(1/4) T '= T
(1/4) U '= U
Therefore, the points are proportional and the proportionality constant is:
k = 1/4
Answer:
Yes; the corresponding sides are proportional.