Question

YW is the perpendicular bisector of ZT.
If TW = 3, YW = 8, and XZ = 12. Find XY.

Answer 1

Answer:

XY = 17 UNIT

Step-by-step explanation:

Given:

TW = 3

YW = 8

XZ = 12

Find:

XY

Computation:

TW = ZW = 3

So,

XW = 12 + 3

XW = 15

So

XY = √XW²+YW²

XY = √15²+8²

XY = √289

XY = 17 UNIT

Answer 2

Applying the definition of perpendicular bisector and the Pythagorean Theorem, the value of XY is calculated as: 17 units.

Recall:

• A perpendicular bisector of a line divides a line segment into two equal halves.

• Also, it forms two opposite right angles on the point of bisection.

Considering the diagram attached below, we are given that:

$TW = 3\\\\YW = 8\\\\XZ = 12$

• We need to find the length of XY.

Applying the Pythagorean theorem:

$XY = \sqrt{XW^2 + YW^2}$

XW = XZ + WZ

XZ = 12 (given)

WZ = TW = 3 (congruent segments)

• Thus:

XW = 12 + 3

XW = 15

Plug in the values of XW and YW into $XY = \sqrt{XW^2 + YW^2}$

• Thus:

$XY = \sqrt{15^2 + 8^2}\\\\\mathbf{XY = 17}$

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