PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.2, Problem 21E
Solution

Find the perimeter and area of the figure determined by the points.

Perimeter = 4(5+4)

Area = 32

Given information:

The given points are (-3,-1), (-1, 3) (7, 3) (5,-1)

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 for calculating perimeter and area.

Calculation:

The given points are A(-3,-1), B(-1, 3) C(7, 3) D(5,-1)

Plotting the points in the graph -

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.2, Problem 21E

Perimeter of enclosed figure ABCD is = AB+BC+CD+DA

Using distance formula −

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

  AB=(x1−x2)+(y1−y2)=(−3−(−1))2+(−1−3)2=(−2)2+(−4)2=4+16=20=25

AB = CD

So CD = 25

B(-1, 3) C(7, 3)

  BC=(x1−x2)+(y1−y2)=(−1−7)2+(3−3)2=(−8)2+(0)2=64=8

BC=DA

So DA=8

Perimeter of enclosed figure ABCD-

   AB+BC+CD+DA=25+25+8+8=45+16=4(5+4)

Area of enclosed figure ABCD is −

As AB=CD and BC=DA

And AB || CD and BC || DA

Therefore ABCD is a parallelogram.

Area of parallelogram ABCD = base⋅height

Base = AD =8

Height = 4

  Area=base⋅height=8⋅4=32

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Chapter P.2, Problem 20E
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Chapter P.2, Problem 22E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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