Coordinate Proofs Worksheet

This worksheet focuses on coordinate proofs, including proving properties of geometric figures using coordinate geometry.

Grade 12 Math GeometryCoordinate Proofs

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Includes

3 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.D.6CCSS.MATH.CONTENT.HSG.GPE.B.4

Topics

mathgeometrycoordinate proofsgrade 12

7 sections · Free to use · Printable

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Read each question carefully and provide clear, step-by-step solutions for each coordinate proof. Show all your work.

1. The vertices of a quadrilateral are A(0,0), B(a,0), C(a+b, c), and D(b,c). Prove that the quadrilateral is a parallelogram.

2. The vertices of a triangle are P(0,0), Q(2a,0), and R(a, 2b). Prove that the medians to the congruent sides are equal in length.

3. To prove that a quadrilateral is a rectangle using coordinate geometry, you must show that its opposite sides are parallel and its diagonals are .

4. The midpoint formula is used to find the coordinates of the of a line segment.

5. The distance formula is derived from the theorem.

6. The slopes of perpendicular lines are negative reciprocals of each other.

True

False

7. Given points A(1, 2), B(4, 2), C(4, 5), and D(1, 5). Prove that ABCD is a square.