PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: Demana
Publisher: PEARSON
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Chapter P.2, Problem 54E
Solution

Prove that the triangle determined by the points (3, 0), (-1, 2), and (5, 4) is isosceles but not equilateral.

The two sides are equal and third one is different so it is an isosceles triangle not an equilateral triangle.

Given information:

The given points (3, 0), (-1, 2), and (5, 4).

Concept used:

  • First, find the value for x on the x-axis.
  • Next, find the y-value on the y-axis.
  • The point should be plotted at the intersection of x and y.
  • Finally, plot the point on your graph at the appropriate spot.
  • Then join all the points to make a closed figure.

Calculation:

The given points A(3, 0), B(-1, 2), and C(5, 4).

Plotting the points in the graph -

  PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA), Chapter P.2, Problem 54E

Using distance formula −

A(3, 0), B(-1, 2)

  AB=(x1−x2)+(y1−y2)=(3−(−1))2+(0−2)2=(4)2+(−2)2=16+4=20

B(-1, 2), C(5, 4)

  BC=(x1−x2)+(y1−y2)=(−1−5)2+(2−4)2=(−6)2+(−2)2=36+4=40

A(3, 0), C(5, 4).

  CA=(x1−x2)+(y1−y2)=(3−5)2+(0−4)2=(−2)2+(−4)2=4+16=20

AB = CA = 20

BC = 40

So the two sides AB=CA are equal and third side BC is different.

Therefore ABC is an isosceles triangle not an equilateral because equilateral triangle have all sides same.

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Chapter P.2, Problem 53E
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Chapter P.2, Problem 55E

Chapter P Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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