Coordinate Geometry Proofs

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Show your work for each problem.

1.
Which formula should you use to prove that two sides of a quadrilateral are equal in length?
1. a)Slope formula
2. b)Quadratic formula
3. c)Midpoint formula
4. d)Distance formula
2.
Two lines are perpendicular if their slopes multiply to:
1. a)
2. b)
3. c)undefined
4. d)
3.
Find the slope of the line passing through and .
4.
Find the distance between and .
5.
What does it mean if two lines have the same slope?
1. a)They are the same line
2. b)They are perpendicular
3. c)They are parallel
4. d)They intersect at the origin
6.
Find the midpoint of the segment with endpoints and . Enter as .
7.
Prove that with and is parallel to with and .
8.
To prove that a quadrilateral is a rhombus using coordinates, what must you show?
1. a)All four sides have equal length
2. b)All angles are 90 degrees
3. c)Diagonals are equal
4. d)Opposite sides are parallel
9.
Prove that lines with slopes and are perpendicular.
10.
Find the distance between and .
11.
Verify that quadrilateral with , , , is a rectangle by showing adjacent sides are perpendicular.
12.
Prove that quadrilateral with , , , is a parallelogram by showing diagonals bisect each other.
13.
If has slope , what slope must have to be perpendicular to ? Enter as a fraction.
14.
Prove that quadrilateral with vertices , , , is a square.
15.
Which property distinguishes a rectangle from a general parallelogram?
1. a)Diagonals bisect each other
2. b)Adjacent sides are perpendicular
3. c)Opposite sides are equal
4. d)Opposite sides are parallel