Coordinate Geometry

See Proof in own window (easier to see whole proof)

See Proof in own window (easier to see whole proof)

See Proof in own window (easier to see whole proof)

Prove that A(0,0), B (3,4) , C (7,9) and D (4,5) be a parallelogram?

Answer

To solve this problem use coordinate geometry proof.

• 1) Use the slope formula. The slope of a line = rise/run to establish that opposite sides are parallel

2) Show all work
• The slope of AB = 4/3
• The slope of CD = (9−5)/(7−4) = 4/3
• The slope of AD = 5/4
• The slope of CB= (9 − 4)/(7− 3) = 5/4

Draw a conclusion
• AB || CD and AD || CB because both pairs of opposite sides have the equal slope.
• ABCD is a parallelogram since the opposite sides are parallel