# Coordinate Geometry

Using the coordinate plane in proof

##### Coordinate Proof 1

Prove that $$XY \perp XC$$

Remember your lesson on perpendicular lines .

##### Coordinate Proof 2

Prove that ABCD is a rectangle.

##### Coordinate Proof 3

Prove that ABCD is a trapezoid that is not isosceles.

Step 1

To solve this problem use coordinate geometry proof.

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

Step 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
Step 3

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