Explanation Given: Given triangle A B C , with vertices A ( 0 , 0 ) , B ( 6 , 0 ) and C ( 0 , 8 ) . Approach: Using the formula of Slope of B C = y 2 − y 1 x 2 − x 1 . Calculation: We need to write the equations of the perpendicular bisector of each of the sides of the triangle. Find perpendicular bisectors of B C . Slope of B C = y 2 − y 1 x 2 − x 1 = 8 − 0 0 − 6 = − 8 6 So, slope of perpendicular bisectors must be reciprocal of slope of B C with opposite sign. Slope of perpendicular bisectors of B C = 6 8 = 3 4 Find mid-point of B C . midpoint = ( 6 + 0 2 , 0 + 8 2 ) = ( 3 , 4 ) Equation of perpendicular bisector is, ( y − y 1 ) = m ( x − x 1 ) So, y − 4 = 3 4 ( x − 3 ) 4 y − 16 = 3 x − 9 4 y − 3 x = 7 y = 3 4 x + 7 4 Find perpendicular bisectors of A C . Slope of A C = y 2 − y 1 x 2 − x 1 = 8 − 0 0 − 0 = undefined So, slope of perpendicular bisectors must be reciprocal of slope of A C with opposite sign To determine b. To find: The coordinates of the intersection of the perpendicular bisectors. To determine c. To find: The radius of the circumcircle for the triangle To determine d. To find: The centre of the circumcircle for the triangle.

Problem Solving Approach to Mathematics for Elementary School Teachers, A, Plus MyLab Math -- Access Card Package (12th Edition)

12th Edition

ISBN: 9780321990594

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Question

Chapter 14.3B, Problem 21A

To determine

a.

To find:

The equations of the perpendicular bisector of each of the sides of the triangle.

To determine

b.

To find:

The coordinates of the intersection of the perpendicular bisectors.

To determine

c.

To find:

The radius of the circumcircle for the triangle

To determine

d.

To find:

The centre of the circumcircle for the triangle.

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Chapter 14.3B, Problem 20A

Chapter 14.3B, Problem 22A

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Chapter 14 Solutions

Problem Solving Approach to Mathematics for Elementary School Teachers, A, Plus MyLab Math -- Access Card Package (12th Edition)

Ch. 14.1 - In track, the second lane from the inside of the...Ch. 14.1 - Prob. 3MC Ch. 14.1 - Observe that it is possible to build a triangle...Ch. 14.1 - a. Help each person in the group find his or her...Ch. 14.1 - Jerry wants to design a gold chain 60 cm long made...Ch. 14.1 - A student claims that the circumference of a...Ch. 14.1 - A student asks why 227 cannot always be used as...Ch. 14.1 - A Student imagines a wire stretched around Earth....Ch. 14.1 - Which of these units would be the best to use to...Ch. 14.1 - If Freds rope is 12 inches long, about how long is...

Knowledge Booster

a. To find: The equations of the perpendicular bisector of each of the sides of the triangle.

a. To find: The equations of the perpendicular bisector of each of the sides of the triangle.

b. To find: The coordinates of the intersection of the perpendicular bisectors.

c. To find: The radius of the circumcircle for the triangle

d. To find: The centre of the circumcircle for the triangle.

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Chapter 14 Solutions

a.

To find:

The equations of the perpendicular bisector of each of the sides of the triangle.

b.

To find:

The coordinates of the intersection of the perpendicular bisectors.

c.

To find:

The radius of the circumcircle for the triangle

d.

To find:

The centre of the circumcircle for the triangle.