Answered: How do you use the midpoint distance or…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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How do you use the midpoint distance or slope formulas to help classify polygon's on the coordinate plane

Expert Solution

Step 1

The slope of two lines are equal when they are parallel to each other while if the product of two lines is -1, then, the lines are perpendicular to each other.

Let's do classification of quadrilaterals (polygon's with 4 sides):

The classification of polygon's can be done as follows:

(i) Check whether the opposite sides of polygon have equal slopes or unequal slopes. If two sides are parallel and other two are non-parallel, then it is a trapezium.

(ii) If no pair of opposite sides are parallel it is scalene quadrilateral.

(iii) If the opposite sides have equal slopes, then, opposite sides are parallel and it is a parallelogram. Also, the mid-points of diagonals will be same.

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