PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Coordinate Geometry
Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …
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Chapter P.2, Problem 37E
Solution

Prove that the figure determined by the points is an isosceles triangle: (1, 3), (4, 7), (8, 4)

The two sides are equal and third one is different so it is an isosceles triangle.

Given information:

The given points (1, 3), (4, 7), (8, 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(1, 3), B(4, 7), C(8, 4)

Plotting the points in the graph -

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.2, Problem 37E

Using distance formula −

A(1, 3), B(4, 7)

  AB=(x1−x2)+(y1−y2)=(1−4)2+(3−7)2=(−3)2+(−4)2=9+16=25=5

B(4, 7), C(8, 4)

  BC=(x1−x2)+(y1−y2)=(4−8)2+(7−4)2=(−4)2+(3)2=16+9=25=5

A(1, 3), C(8, 4)

  CA=(x1−x2)+(y1−y2)=(1−8)2+(3−4)2=(−7)2+(−1)2=49+=50=52

AB = BC=5

CA = 52

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

Therefore ABC is an isosceles triangle having two sides same and one is different.

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Chapter P.2, Problem 36E
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Chapter P.2, Problem 38E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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