Page 102 - Math Course 3 (Book 2)

Coordinate Proofs

Your Turn!

Position and Label a Triangle
Which picture on the following slide would be the best way to position and label equilateral triangle ABC
with side BC w units long on the coordinate plane?

A( w, v)
A. B.

2
C . B( , v) D . A( , v)
w
w
2

Answer

Find the Missing Coordinates Coordinate Proof

Name the missing coordinates of isosceles right Finish the following coordinate proof to prove that
ΔABC. the segment drawn from the right angle to the
midpoint of the hypotenuse of an isosceles right

y triangle is perpendicular to the hypotenuse.
y
A(?, ?)
A(0, 2a)

D(?, ?)

O C(0, 0) B(2a, 0) X

Proof: The coordinates of the midpoint D, are
O C(?, ?) B(d, 0) X ( , ) or (a, a). The slope of CD
0 + 2a
2a + 0
2
2
0 – a
2a – 0
is ( ) or 1. The slope of AB is ( )
A. A(d, 0); C(0, 0) 0 – a 0 – 2a
B. A(0, f); C(0, 0) or –1 therefore CD ⟂ AB because_______.
C. A(0, d); C(0, 0)
D. A(0, 0); C(0, d) A. their slopes are opposite.
B. the sum of their slopes is zero.
C. the product of their slopes is –1.
D. the difference of their slopes is 2.
Answer
Answer

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