Question

In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?

a.) EF = 6 cm and FG = 10 cm
b.) EF = 7 cm and FG = 3 cm
c.) EF = 15 cm and FG = 20 cm
d.) EF = 25 cm and FG = 35 cm
Please show your work. Thanks!

Answer 1

D. EF= 25 cm and fg = 35 cm

Explanation:

I did this on a quiz. I got it right.

Answer 2

Answer is D

After dilation the image remain same but it is stretched or shrinked to the original size.

That means the ratio of the sides and the angles between the sides remain same .

Here we did dilation of ABCD which made it to EFGH.

Hence the ratio of the corresponding sides of the original rectangle ABCD should remain same even after dilation.

the corresponding sides are : AB and EF

BC and FG

CD and GH

DA and HE

* Let us find ratio of the sides AB and BC

given that AB= 10 and BC= 14

AB/BC= 10/14 = 5 /7 ( 10 and 14 both are multiple of 2 so we reduced them by a factor of 2 )

* the raio of the corresponding sides EF and FG should be same ( 5/7)

in the option D EF= 25 and FG= 35

so EF/FG= 25/35 = 5 /7 ( both are multiple of 5 so we reduced them by the factor of 5 )

Since ratio of the corresponding sides are coming out to be same for the EFGH given in option D it should be the dilation of the ABCD