Page 26 - Math Course 3 (Book 2)

Properties of Rectangles

Method 2: Use the Distance Formula
DB = [4–(–1)] + [3 –( –2)] 2
2
d = (x –x ) + (y –y ) 2
2
2 1 2 1
to determine whether opposite = 25 + 25
sides are congruent.
= 50

B(4, 3) The length of each diagonal is 50

A(–2, 1)
Since the diagonals are
D(5, 0) Answer congruent, ABCD is a rectangle.

Your Turn!
D(–1, –2)

Rectangle on a Coordinate Plane
Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3),
AB = [4–(–2)] + (3 – 1) 2 Y(3, 1), and Z(2, –1). Determine whether WXYZ is a
2
rectangle using the Distance Formula.
= 36 + 4
A. yes
= 40 B. no
C. cannot be determined

CD = [5–(–1)] + [0 – (–2)] 2
2
Answer
= 36 + 4

= 40

AD = [–1 – (–2)] + (–2 – 1) 2
2
= 1 + 9

= 10 What are the lengths of diagonals WY and XZ?

A. 5
2
BC = (5 – 4) + (0 – 3) 2 B. 4
= 1 + 9 C. 5
D. 25
= 10

Since each pair of opposite sides of the quadrilat- Answer
eral have the same measure, they are congruent.
Quadrilateral ABCD is a parallelogram.

Find the length of the diagonals.

AC = [5–(–2)] + (0 – 1) 2
2
= 49 + 1

= 10

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