Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a.

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Presentation transcript:

Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a figure in the coordinate plane is a parallelogram, rhombus, rectangle, square, or trapezoid.

Example Given points: A(0,2) B(3,6) C(8,6) D(5,2) How can we prove ABCD is a parallelogram, rectangle, rhombus, or a square?

Slope Formula Given: (x 1,y 1 ) (x 2,y 2 ) *Perpendicular lines have opposite reciprocal slopes ex: m = 3/2 & -2/3 *Parallel lines have the same slope ex: m = 3 & 3

Example A(0,2) B(3,6) C(8,6) D(5,2) Step 1: Is ABCD a parallelogram? *check to see if slopes are parallel

Example A(0,2) B(3,6) C(8,6) D(5,2) Step 2: Is ABCD a rectangle or a square? *were the slopes perpendicular?

Distance Formula Given: (x 1,y 1 ) (x 2,y 2 ) OR…. Use the Pythagorean Theorem on a grid

Example A(0,2) B(3,6) C(8,6) D(5,2) Step 3: Is ABCD a rhombus? *check the lengths