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Math
GeometryElementary Geometry For College Students, 7e7th Edition

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Chapter 10.3, Problem 39E
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
BuyFindarrow_forward

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·(a−2)a

x=2a-4

This is the distance between T and V

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Chapter 10.3,
Problem 38E
Chapter 10.3,
Problem 40E
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