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: W' (6, 0); X' (0, 0); Y' (0, 12); Z' (6,12). Is the design of the cover similar to the actual cover?

Answer 1

No; the corresponding sides are not proportional.

Answer 2

Answer: Not similar

Step-by-step explanation:

From the given graph, by using distance formula

For figure WXYZ with coordinates W(2,0), X(0,0), Y(0,3) and Z(2,3)

Since, YX is on y axis, then length of YX=$|3-0|=3\ units$

Similarly, WX is on x axis, then length of WX=$|2-0|=2$

Now, for W'X'Y'Z' with coordinates W' (6, 0); X' (0, 0); Y' (0, 12); Z' (6,12), the length of W'X'=$\sqrt{(6-0)^2+(0)^2}=6\ units$

The length of Y'X'=$\sqrt{(0)^2+(0-12)^2}=12\ units$

We know that if two figures are similar then their corresponding sides are proportional.

Now, $\frac{YX}{Y'X'}=\frac{3}{12}=\frac{1}{4}$

$\frac{WX}{W'X'}=\frac{2}{6}=\frac{1}{3}$

But, $\frac{1}{4}\neq\frac{1}{3}$,

Hence they are not proportional so they are not similar.