   Chapter 10.3, Problem 39E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Δ R S T , S V - bisects ∠ R S T . Find the coordinates of point T in terms of a . To determine

To find:

The coordinates of point T in terms of a.

Explanation

The given figure is shown below.

This is solved by angle bisector theorem.

Angle bisector theorem states that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

From the diagram,

TVTS=VRRS

Let the distance between T and V be x.

TS=2a

RS=a

To find VR, use the distance formula.

x1,y1=V2, 0

x2,y2=Ra, 0

Formula for distance between two points

d=x2-x12+y2-y12

Substituting the x and y co-ordinates

d=a-22+0-02

On solving this,

d=a-22+02

d=a-22

Taking square root,

d=a-2

Substitute the values in the theorem statement,

xa-2=2aa

Solving for x,

x=2a·a-2a

Cancelling a,

x=2a·(a2)a

x=2a-4

This is the distance between T and V

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