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 38E
Solution

a.

The prove that the diagonals of the figure determined by the given points bisect each other.

Given:

Square, −7,−1, −2,4, 3,−1, −2,−6

Calculation:

In order to prove that the diagonals of the square defined by the given points, show that the midpoint of the diagonals connecting the opposite corners is the same. That is, the midpoint of the diagonal connecting the vertices −7,−1,  3,−1 and the midpoint of the diagonal connecting the vertices −2,4, −2,−6 are same.

  Midpoint of −7,−1 and 3,−1=Midpoint of −2,4 and −2,−6−7+32,−1+−12=−2+−22,4+−62−42,−22=−42,−22−2,−1=−2,−1 True statement

Since the midpoints of the diagonals are same, it implies that the diagonals of the square bisect each other.

b.

The prove that the diagonals of the figure determined by the given points bisect each other.

Given:

Parallelogram −2,−3, 0,1, 6,7, 4,3

Calculation:

In order to prove that the diagonals of the parallelogram defined by the given points, show that the midpoint of the diagonals connecting the opposite corners is the same. That is, the midpoint of the diagonal connecting the vertices −2,−3, 6,7 and the midpoint of the diagonal connecting the vertices 0,1, 4,3 are same.

  Midpoint of −2,−3 and 6,7=Midpoint of 0,1 and  4,3−2+62,−3+72=0+42,1+3242,42=42,422,2=2,2 True statement

Since the midpoints of the diagonals are same, it implies that the diagonals of the parallelogram bisect each other.

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Chapter P.2, Problem 37E
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Chapter P.2, Problem 39E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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