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.

Which statement is correct about the two kites?
A) They are similar because Line BR : Line DB is 1:2 and line KE : Line YK 1:2.

B) They are similar because Line BR : Line DB is 2:1 and Line KE : Line YK is 2:1.

C) They are not similar because Line BR : Line DB is 1:2 and Line KE : Line YK is 2:1.

D: They are not similar bcause Line BR : Line DB and Line KE : Line YK is 1:2.

Answer 1

the answer is the option A

They are similar because Line BR : Line DB is
`1:2` and line KE : Line YK
`1:2`

Explanation:

we know that

If the figures are similar

then

the ratio of their corresponding figures are equal

so

`(BR)/(KE)=(DB)/(YK)`

Find the distances

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance BR

substitute the values

`d=\sqrt{(4-6)^(2)+(6-5)^(2)}`

`d=\sqrt{(-2)^(2)+(1)^(2)}`

`dBR=√(5)\ units`

Find the distance KE

substitute the values

`d=\sqrt{(11-9)^(2)+(10-6)^(2)}`

`d=\sqrt{(2)^(2)+(4)^(2)}`

`dKE=2√(5)\ units`

Find the distance DB

substitute the values

`d=\sqrt{(6-4)^(2)+(5-1)^(2)}`

`d=\sqrt{(2)^(2)+(4)^(2)}`

`dDB=2√(5)\ units`

Find the distance YK

substitute the values

`d=\sqrt{(9-1)^(2)+(6-10)^(2)}`

`d=\sqrt{(8)^(2)+(-4)^(2)}`

`dYK=4√(5)\ units`

substitute

`(BR)/(KE)=(DB)/(YK)`

`(√(5))/(2√(5))=(2√(5))/(4√(5))`

`(1)/(2)=(2)/(4)`

`(1)/(2)=(1)/(2)` --------> the figures are similar

`(BR)/(KE)=(DB)/(YK)`-----> rewrite

`(BR)/(DB)=(KE)/(YK)`

substitute the values

`(√(5))/(2√(5))=(2√(5))/(4√(5))`

simplify

`(1)/(2)=(2)/(4)` ------>
`(1)/(2)=(1)/(2)`