Geometry 1
Homework on Coordinate Proofs
Name: _________________________________
Problems 1-3: Graph the quadrilaterals with the following vertices, find the slopes of the sides
(write the slopes above each side), then refer to the slopes to answer the questions.
ABCD : A = (–6, 2) B = (0, –5) C = (7, 1) D = (2, 8)
EFGH
KLMN
:
:
E
K
= (–8, 0)
= (9, 7)
F
L
= (–3, 8)
= (0, 9)
PQRS : P = (–6, 5) Q = (4, 10) y y x x
1. Which of the quadrilaterals are parallelograms?
G
M
R
= (5, 4)
= (–6, –2)
= (8, 2) y y
H
N
S
= (0, –4)
= (3, –4)
= (–2, –3) x x
2. Which of the quadrilaterals are rectangles?
3. Which of the quadrilaterals are squares?
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Problems 4-7: The vertices of quadrilateral ABCD have the following coordinates:
A = (0, –7) B = (6, –3) C = (10, 11) D = (–10, 5)
Points M, N, P, and Q are the midpoints of sides AB, BC, CD, and AD , respectively.
4. Plot these points and draw quadrilateral ABCD :
y
x
5. Give the coordinates of the midpoints:
M = ________ N = ________ P = ________ Q = ________
6. Prove that quadrilateral MNPQ is a parallelogram by showing its opposite sides have the same slopes.
7.
Is quadrilateral MNPQ a rectangle? Why or why not?
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8. Suppose points A and B have the following coordinates: A (–5, 2), B (0, 14). a. What are the coordinates of the midpoint of AB ? b. What is the length of AB ?
9. Suppose points C and D have the following coordinates: C (4, –7), D (4, 3). a. What are the coordinates of the midpoint of CD ? b. What is the length of CD ?
10. Suppose point M is the midpoint of PQ , and points M and Q have coordinates M (–5, 6), Q (3, 9). a. What are the coordinates of point P ? b. What is the length of PQ ?
Problems 11-14: Supply the missing coordinates without introducing any new letters.
11. ABCD is a square: 12.

PQR is isosceles: y
B (?, ?) C (?, ?)
A
D ( a , 0)
13. MNOP is a parallelogram: x y
P ( c , ?) M (?, a )
O
N ( b , ?) x
14. y
P
DEFG y
G
D
is a rectangle:
(?, k
Q
)
( b , c )
R
F
(?, ?)
(
E m
(?, ?)
, ?) x x
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15. Use the trapezoid to on the right to prove: a.
The median is parallel to the bases. y
T b. The length of the median is the average of the base-lengths.
R (2 a , 2 b ) A
P
(2
(2 c d
, 2 b
, 0)
) x
16. Use the parallelogram below to prove the sum of the squares of the lengths of the sides of s parallelogram is equal to the sum of the squares of the lengths of the diagonals. y
A
B ( a , h )
D ( c
C
, 0)
( b x
, h )
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