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: H' (10,0); I' (0, 0); J' (0, 16); K' (10,16). Is the design of the cover similar to the actual cover?

The coordinates of the corners in the scale drawing of the desing are:

H = (2,0)

I = (0,0)

J = (0,4)

K = (2,4)

That makes the lengths of the segments be:

HI = 2 - 0 = 2

JK = 2 - 0 = 2

JI = 4 - 0 = 4

KH = 4 - 0 = 4

Now check the segments of the actual cover:

H'I' = 10 - 0 = 10

K'J' = 10 - 0 = 10

J'I' = 16 - 0 = 16

K'H' = 16 - 0 = 16

Now check corresponding segments meet proportionality criterium, which is needed for similarity:

H'I' / HI = 10 / 2 = 5

K'J' / KJ = 10 / 2 = 5.

So far we this is fine.

JI / J'I' = 16 / 4 = 4 ... then not, the ratio is not the same ratio of the other two segments, which implies that the scale used for the vertical segments is different to the scale used for the horizontal segments, driving to a non similar figure.

Answer: no, because the corresponding sides are not proportional