Question

Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coordinate plane as kites BRAD and KELY, respectively:
Kite BRAD has the following coordinates: B is at point 3,7; R is at 4, 6; A is at point 3, 3; D is at point 2, 6. Kite KELY has the following coordinates: K is at point 11, 2; E is at point 9, 0; L is at point 3, 2; Y is at point 9,4.

Which statement is correct about the two kites?

A. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 1:2.
B. They are not similar because the corresponding sides of kites KELY and BRAD all have the relationship 1:2.
C. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.
D. They are not similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.

I think C because it says KELY and BRAD, not BRAD and KELY. I also know that they are similar. Let me know if I'm correct.

Answer 1

The correct answer is:

C. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.

Using the distance formula,

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

the lengths of the sides of BRAD are:

$\text{BR}=\sqrt{(7-6)^2+(3-4)^2}=\sqrt{1^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}\\\\\text{RA}=\sqrt{(6-3)^2+(4-3)^2}=\sqrt{3^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{AD}=\sqrt{(3-6)^2+(3-2)^2}=\sqrt{(-3)^2+1^2}=\sqrt{9+1}=\sqrt{10}\\\\\text{DB}=\sqrt{(6-7)^2+(2-3)^2}=\sqrt{(-1)^2+(-1)^2}=\sqrt{1+1}=\sqrt{2}$

The lengths of the sides of KELY are:

$\text{KE}=\sqrt{(2-0)^2+(11-9)^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}\\\\\text{EL}=\sqrt{(0-2)^2+(9-3)^2}=\sqrt{(-2)^2+6^2}=\sqrt{40}=2\sqrt{10}\\\\\text{LY}=\sqrt{(2-4)^2+(3-9)^2}=\sqrt{(-2)^2+(-6)^2}=\sqrt{40}=2\sqrt{10}\\\\\text{YK}=\sqrt{(4-2)^2+(9-11)^2}=\sqrt{2^2+(-2)^2}=\sqrt{8}=2\sqrt{2}$

Each side of KELY is twice the length of the corresponding side on BRAD.  This makes the ratio of the sides 2:1 and the figures are similar.

Answer 2

The correct answer is 'they are not similar because line BR : line DB is 1 : 2 and line KE : line YK is 1 : 3'. This is correct because I took the test and got it right.