How would you use the distance formula to show that a parallelogram is a rectangle?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 7RE
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How would you use the distance formula to show that a parallelogram is a rectangle?

Cio, 41
BI5,4)
d = Jx - x) + V2 - Yı).
%3D
In the figure at the right, the length of AB is
V(5-1) +(4-1) =4? +3
=5.
%3D
In the figure above right the length of BC is
/(5-0) + (4- 4) = 52 +0? =5.
So, AB = BC. The figure is an isosceles triangle.
To find the midpoint of a side or diagonal, use the Midpoint Formula.
X+ X2 Y1+ Y2
M =
2 2
(1+5 1+4
6 5
In the figure above, the midpoint of AB is
2 2
To determine whether line segments that form sides or diagonals are parallel
or perpendicular, use the Slope Formula.
m =
X2 - X
(4 –1) _ 3
(5-1) 4
In the figure at the right, the slope of AB is
ty
S(5, 6)
T(1, 3)
B(5, 4)
(6 – 3) 3
(5-1) 4
The slope of TS is
The line segments are
%3D
parallel.
A(1, 1)
Lines with equal slopes are parallel.
Transcribed Image Text:Cio, 41 BI5,4) d = Jx - x) + V2 - Yı). %3D In the figure at the right, the length of AB is V(5-1) +(4-1) =4? +3 =5. %3D In the figure above right the length of BC is /(5-0) + (4- 4) = 52 +0? =5. So, AB = BC. The figure is an isosceles triangle. To find the midpoint of a side or diagonal, use the Midpoint Formula. X+ X2 Y1+ Y2 M = 2 2 (1+5 1+4 6 5 In the figure above, the midpoint of AB is 2 2 To determine whether line segments that form sides or diagonals are parallel or perpendicular, use the Slope Formula. m = X2 - X (4 –1) _ 3 (5-1) 4 In the figure at the right, the slope of AB is ty S(5, 6) T(1, 3) B(5, 4) (6 – 3) 3 (5-1) 4 The slope of TS is The line segments are %3D parallel. A(1, 1) Lines with equal slopes are parallel.
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