Respuesta :
Answer:
y = -7
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
[tex]\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}[/tex]Since AB = CD hence;
[tex]\text{ }\sqrt[]{37\text{ }}=\sqrt[]{y^2+16y+100}[/tex]Square both sides
[tex]\begin{gathered} (\text{ }\sqrt[]{37\text{ )}^{}}^2=(\sqrt[]{y^2+16y+100})^2 \\ 37=\text{ }y^2+16y+100 \end{gathered}[/tex]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
