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 19E
Solution

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

Perimeter = 241+82

Area = −412

Given information:

The given points are (-5, 3), (0,-1) (4, 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 for calculating perimeter and area.

Calculation:

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

Plotting the points in the graph -

  PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA), Chapter P.2, Problem 19E

Perimeter of enclosed figure ABC is = AB+BC+CA

Using distance formula −

A(-5, 3), B(0,-1)

  AB=(x1−x2)+(y1−y2)=(−5−0)2+(3−(−1))2=(−5)2+(4)2=25+16=41

B(0,-1), C(4, 4)

  BC=(x1−x2)+(y1−y2)=(0−4)2+(−1−4)2=(−4)2+(−5)2=16+25=41

A(-5, 3), C(4, 4)

  BC=(x1−x2)+(y1−y2)=(−5−4)2+(3−4)2=(−9)2+(−1)2=81+1=82

Perimeter of ABC = AB+BC+CA

   AB+BC+CA=41+41+82=241+82

Area of enclosed figure ABC is −

  Area=12[x1(y3−y2)+x2(y1−y3)+x3(y2−y1)]=12[−5(4−(−1))+0(3−4)+4(−1−3)]=12[−5(5)+0+4(−4)]=12[−25−16]=−412

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Chapter P.2, Problem 18E
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Chapter P.2, Problem 20E

Chapter P Solutions

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

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