Using the Distance Formula in Coordinate Geometry Proofs.

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Presentation transcript:

Using the Distance Formula in Coordinate Geometry Proofs

Given the coordinates of the three vertices of a triangle, use the distance formula to prove that a triangle is isosceles A (-1, -5) B (5,2) C (-3,4)

A B C Observation and Conclusion:

Given the coordinates of the 4 vertices of a quadrilateral, use the distance formula to prove that the quadrilateral is a rhombus C (8,2) A (0, -4) B (5, -4) D (3,2)

C A B D Observation and Conclusion: Since the quadrilateral is equilateral, then the quadrilateral is a rhombus

Given the coordinates of the three vertices of a triangle, use the distance formula to prove that the triangle is a right triangle C (1,15) A (1,7)B (16,7)

C AB Observation and Conclusion: then the Pythagorean Theorem is satisfied. Since the Pythagorean Theorem is satisfied, then the triangle must be a right triangle

The Distance Formula can be used in many other coordinate proofs…

To use the distance formula to prove that a quadrilateral is a parallelogram … C A B D Show that both pairs of opposite sides are congruent

To use the distance formula to prove that a quadrilateral is a rectangle C A B D Show that ABCD is a parallelogram with congruent diagonals