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

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'=
`√((6-0)^2+(0)^2)=6\ units`

The length of Y'X'=
`√((0)^2+(0-12)^2)=12\ units`

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

Now,
`(YX)/(Y'X')=(3)/(12)=(1)/(4)`

`(WX)/(W'X')=(2)/(6)=(1)/(3)`

But,
`(1)/(4)\\eq(1)/(3)`,

Hence they are not proportional so they are not similar.