Question

C. Line m is a perpendicular bisector. If EG=12 and FG=5, of then how long is:

Answer 1

Answer:

$EF = 13$

$GH = 5$

$EH = 13$

Step-by-step explanation:

Given

The attached figure

$EG = 12$

$FG = 5$

Solving (a): EF

Since m is a perpendicular bisector, then <EGF and <EGH are right-angled.

So, EF will be calculated using Pythagoras theorem which states:

$EF^2 = EG^2 + FG^2$

$EF^2 = 12^2 + 5^2$

$EF^2 = 144 + 25$

$EF^2 = 169$

Take the positive square roots of both sides

$EF = \sqrt{169$

$EF = 13$

Solving (b): GH

Since m is a perpendicular bisector, then GH = FG

$FG = 5$

$GH = FG$

$GH = 5$

Solving (c): EH

Since m is a perpendicular bisector, then EH = EF

$EF = 13$

$EH = EF$

$EH = 13$