Question

In rectangle ABCD, AC = -x + 21, BP = -9x + 19, and DP = -y + 5. Find the value of y.

Answer 1

y=-5

Explanation:

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are equal and bisect each other

so

`BP=(1)/(2)AC`

`DP=BP`

step 1

Find the value of x

`BP=(1)/(2)AC`

substitute the given values

`(-9x+19)=(1)/(2) (-x+21)`

solve for x

Multiply by 2 both sides

`-18x+38=-x+21`

`18x-x=38-21\\17x=17\\x=1`

step 2

Find the value of y

`DP=BP`

we have

`BP=-9x+19`

`DP=-y+5`

substitute

`-y+5=-9x+19`

substitute the value of x

`-y+5=-9(1)+19\\-y+5=10\\y=5-10\\y=-5`