Grade 9 Math: Coordinate Proofs
This worksheet focuses on coordinate proofs, including proving geometric properties on a coordinate plane, calculating distances, midpoints, and slopes.
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Coordinate Proofs
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Given the points A(2, 3) and B(8, 11), find the distance between A and B, and the midpoint of the segment AB.
Distance:
Midpoint:
2. Which of the following statements is true about the slopes of parallel lines?
Their slopes are negative reciprocals.
Their slopes are equal.
The product of their slopes is 1.
Their slopes are undefined.
3. To prove that a quadrilateral is a parallelogram using coordinate geometry, you can show that both pairs of opposite sides have the same or that the diagonals each other.
4. Prove that the quadrilateral with vertices P(-2, 1), Q(1, 4), R(4, 1), and S(1, -2) is a rhombus. Show all calculations for distance and slope.
5. The slopes of perpendicular lines are always negative reciprocals of each other, unless one is horizontal and the other is vertical.
True
False
6. Plot the points A(0,0), B(5,0), C(5,3), and D(0,3) on the coordinate plane below. What type of quadrilateral is ABCD? Justify your answer using coordinate geometry principles.
Type of Quadrilateral:
Justification: