Question

For a parallelogram ABCD, the side AB = square root37 units. C is at (2. y) and D is at (-4,-8). Also, y > -8. Find y.

Answer 1

y = -7

Step-by-step explanation:

For a parallelogram ABCD, opposite side AB and CD are parallel.

Given

AB = \sqrt{37}

if C = (2, y) and D = (-4, -8)

Then we need to get the distance between C and D using the distance formula

`\begin{gathered} CD\text{ = }\sqrt[]{(-8-y)^2+(-4-2)^2} \\ CD\text{ }=\text{ }\sqrt[]{(-8-y)^2+(-6)^2} \\ CD\text{ = }\sqrt[]{(64+16y+y^2)+36} \\ CD\text{ = }\sqrt[]{y^2+16y+100} \end{gathered}`

Since AB = CD hence;

`\text{ }\sqrt[]{37\text{ }}=\sqrt[]{y^2+16y+100}`

Square both sides

`\begin{gathered} (\text{ }\sqrt[]{37\text{ )}^{}}^2=(\sqrt[]{y^2+16y+100})^2 \\ 37=\text{ }y^2+16y+100 \end{gathered}`

Equate to zero

y^2+16y+100-37 = 0

y^2+16y+63 = 0

Factorize

y^2+7y+9y+63 = 0

y(y+7)+9(y+7) = 0

(y+9)(y+7) = 0

y+9 = 0 and y+7 = 0

y = -9 and y = -7

since y > -8, hence the value of y is -7