Answer to Question #2132 in Geometry for jade
Question #2132
Prove that the quadrilateral ABCD is a rectangle given A(-8, -2) B (-3,3) C (3,-3) D(-2,-8) .
Expert's answer
Let's find the slope from the equations of the lines (y=mx+ b) passing through the points:
AB: A(-8, -2) B (-3,3)& m& = 1
BC: B (-3,3) C (3,-3)& m = -1
CD: C (3,-3) D(-2,-8) m = 1
DA: D(-2,-8) A(-8, -2)& m =-1
Thus AB is parallel to CD, BC is parallel to DA, as their slopes are equal to each other respectively, AB is perpendicular to BC, and BC is perpendicular to CD, as m(AB) = -m(BC) nad m(BC) = -m (CD). This shows that ABDC is a rectangle.
AB: A(-8, -2) B (-3,3)& m& = 1
BC: B (-3,3) C (3,-3)& m = -1
CD: C (3,-3) D(-2,-8) m = 1
DA: D(-2,-8) A(-8, -2)& m =-1
Thus AB is parallel to CD, BC is parallel to DA, as their slopes are equal to each other respectively, AB is perpendicular to BC, and BC is perpendicular to CD, as m(AB) = -m(BC) nad m(BC) = -m (CD). This shows that ABDC is a rectangle.
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