Question

WLL GIVE BRAINLIST PLEASE help... i sincerely don't even know where to begin here. ​

Answer 1

Answer:

y = 5

Step-by-step explanation:

WY is the perpendicular bisector of XZ and so divides ΔWXZ into 2 congruent triangles ΔWXY and ΔWZY

Hence WZ = WX ← corresponding sides, thus

5y - 8 = 2y + 7 ( subtract 2y from both sides )

3y - 8 = 7 ( add 8 to both sides )

3y = 15 ( divide both sides by 3 )

y = 5

Answer 2

Answer:

y = 5

Step-by-step explanation:

"The perpendicular bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment."

It means:

$\overline{XY}=\overline{YZ}\\2x+3=3x-5\\2x-3x=-5-3\\-x=-8\\x=8$

Checking

$\overline{XY}=2x+3\\\overline{XY}=2(8)+3\\\overline{XY}=16+3\\\overline{XY}=19$

$\overline{YZ}=3x-5\\\overline{YZ}=3(8)-5\\\overline{YZ}=24-5\\\overline{YZ}=19$

Now, WY divides the triangle, forming two rectangular triangles, then:

$(\overline{WZ})^2=(\overline{YZ})^2+(\overline{WY})^2\\(5y-8)^2=(19)^2+(\overline{WY})^2\\(5y-8)^2=361+(\overline{WY})^2\\(5y-8)^2-361=(\overline{WY})^2\\\\ (\overline{WY})^2=(5y-8)^2-361\\\overline{WY}=\sqrt{(5y-8)^2-361}$

$(\overline{WX})^2=(\overline{WY})^2+(\overline{XY})^2\\({2y+7})^2=(\overline{WY})^2+({19})^2\\({2y+7})^2=(\overline{WY})^2+361\\({2y+7})^2-361=(\overline{WY})^2\\\\ (\overline{WY})^2=({2y+7})^2-361\\\overline{WY}=\sqrt{({2y+7})^2-361}$

We know that WY has the same value in both equations, then:

$\sqrt{({2y+7})^2-361}=\sqrt{(5y-8)^2-361}\\({2y+7})^2-361=(5y-8)^2-361\\({2y+7})^2=(5y-8)^2\\2y+7=5y-8\\2y-5y=-8-7\\-3y=-15\\\\ y=\frac{-15}{-3}\\\\ y=5$