Page 41 - Math Course 3 (Book 2)

Quadrilaterals: Coordinate Proofs

Find Missing Coordinates

Name the missing coordinates for the parallelogram. y

A. C(c, c)
B. C(a, c) D(0, c) C(?, ?)
C. C(a + b, c)
D. C(b, c)

Answer

O A(a, 0) B(a + b, 0) X

Coordinate Proof

Place an isosceles trapezoid on the coordinate plane. Label the midpoints of the sides M, N, P, and Q.
Write a coordinate proof to prove that MNPQ is a rhombus.

Given: ABCD is an isosceles trapezoid. y
M, N, P, and Q are midpoints.

Prove: MNPQ is a rhombus.
B(–2a, 2b) Q C(2a, 2b)
Proof: The coordinates of M are (–3a, b); the
coordinates of N are (0, 0); the coordinates of
P are (3a, b); the coordinates of Q are (0, 2b) M P

Since opposite sides have equal slopes, opposite sides
are parallel and MNPQ is a parallelogram. The slope of x
MP is 0. The slope of NQ is undefined. So, the diagonals A(–4a, 0) O N D(4a, 0)
are perpendicular. Thus, MNPQ is a rhombus.

A. √3a + b
B. √3a² + b²
C. √9a² + b²
D. 3a + b
Answer

Coordinate Proof

Find the slope of AB and CD to prove that the crossbars of a child safety gate are parallel.

Given: A(–3, 4), B(1, –4), C(–1, 4), D(3, –4) C(–1, 4)

Prove: AB || CD A(–3, 4)

A. slopes = 2
B. slopes = –4
C. slopes = 4
D. slopes = –2

D(3, –4)
Answer
B(1, –4)

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