Question

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

Answer 1

Answer:

y=-5

Step-by-step 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

$BP=\frac{1}{2}AC$

$DP=BP$

step 1

Find the value of x

$BP=\frac{1}{2}AC$

substitute the given values

$(-9x+19)=\frac{1}{2} (-x+21)$

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

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