Coordinate Geometry

Using the coordinate plane in proof

Coordinate Proof 1

Prove that $$ XY \perp XC $$

Remember your lesson on perpendicular lines .

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Coordinate Proof 2

Prove that ABCD is a rectangle.

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Coordinate Proof 3

Prove that ABCD is a trapezoid that is not isosceles.

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Proof 4

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

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
naxt toEuclidean Proof