a. Explanation Given: The given coordinates are A ( 3 , 3 ) , B ( 6 , 9 ) and C ( 9 , 3 ) . Calculation: Use distance formula. The distance, d units, between two points with coordinates ( p 1 , q 1 ) and ( p 2 , q 2 ) is given by d = ( p 2 − p 1 ) 2 + ( q 2 − q 1 ) 2 . A B = ( 6 − 3 ) 2 + ( 9 − 3 ) 2 = 3 2 + 6 2 = 45 B C = ( 9 − 6 ) 2 + ( 3 − 9 ) 2 = 3 2 + ( − 6 ) 2 = 45 C A = ( 3 − 9 ) 2 + ( 3 − 3 ) 2 = 6 2 = 6 Isosceles triangle → it is a triangle which has at least two sides of equal length. From the above result, A B = B C . Hence the given coordinates represent a isosceles triangle. b. To determine Find the perimeter of the triangle. Answer The perimeter of the isosceles triangle is 19.42 units. Explanation Given: The given coordinates are A ( 3 , 3 ) , B ( 6 , 9 ) and C ( 9 , 3 ) . Calculation: Use distance formula. The distance, d units, between two points with coordinates ( p 1 , q 1 ) and ( p 2 , q 2 ) is given by d = ( p 2 − p 1 ) 2 + ( q 2 − q 1 ) 2 . A B = ( 6 − 3 ) 2 + ( 9 − 3 ) 2 = 3 2 + 6 2 = 45 B C = ( 9 − 6 ) 2 + ( 3 − 9 ) 2 = 3 2 + ( − 6 ) 2 = 45 C A = ( 3 − 9 ) 2 + ( 3 − 3 ) 2 = 6 2 = 6 Isosceles triangle → it is a triangle which has at least two sides of equal length. From the above result, A B = B C . Perimeter of the isosceles triangle p = 2 a + b , where a is the same side and b is the another side. p = 2 45 + 6 = 6 5 + 6 = 6 ( 5 + 1 ) = 6 ⋅ 3.236 = 19.416 ≈ 19.42 Hence the perimeter of the isosceles triangle is 19.42 units.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 10.5, Problem 1MCQ

To determine

Check whether the given coordinates represent a isosceles triangle or not.

Expert Solution

Explanation of Solution

Given:

The given coordinates are A(3,3),B(6,9) and C(9,3) .

Calculation:

Use distance formula.

The distance, d units, between two points with coordinates (p1,q1) and (p2,q2) is given by d=(p2−p1)2+(q2−q1)2 .

AB=(6−3)2+(9−3)2=32+62=45BC=(9−6)2+(3−9)2=32+(−6)2=45CA=(3−9)2+(3−3)2=62=6

Isosceles triangle → it is a triangle which has at least two sides of equal length.

From the above result, AB=BC .

Hence the given coordinates represent a isosceles triangle.

To determine

Find the perimeter of the triangle.

Expert Solution

Answer to Problem 1MCQ

The perimeter of the isosceles triangle is 19.42 units.

Explanation of Solution

Given:

The given coordinates are A(3,3),B(6,9) and C(9,3) .

Calculation:

Use distance formula.

The distance, d units, between two points with coordinates (p1,q1) and (p2,q2) is given by d=(p2−p1)2+(q2−q1)2 .

AB=(6−3)2+(9−3)2=32+62=45BC=(9−6)2+(3−9)2=32+(−6)2=45CA=(3−9)2+(3−3)2=62=6

Isosceles triangle → it is a triangle which has at least two sides of equal length.

From the above result, AB=BC .

Perimeter of the isosceles triangle p=2a+b , where a is the same side and b is the another side.

p=245+6=65+6=6(5+1)=6⋅3.236=19.416≈19.42

Hence the perimeter of the isosceles triangle is 19.42 units.

Chapter 10.5, Problem 45E

Chapter 10.5, Problem 2MCQ

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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