Coordinate Proofs Worksheet
A Grade 11 Math worksheet focusing on coordinate proofs, including distance formula, midpoint formula, and slope to prove geometric properties.
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Topics
Coordinate Proofs: Grade 11 Geometry
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Read each question carefully and provide a complete answer. Show all your work for coordinate proofs.
1. Given points A(-3, 5) and B(7, -1), find the distance between A and B, and the midpoint of the segment AB.
2. State whether each statement is True or False.
True
False
a) The slope of a horizontal line is undefined.
True
False
b) Perpendicular lines have slopes that are negative reciprocals of each other.
3. Prove that the triangle with vertices A(1, 2), B(4, 2), and C(1, 6) is a right-angled triangle using coordinate geometry. Include a sketch of the triangle on the coordinate plane.
4. Which of the following properties is true for a parallelogram but not necessarily for a rhombus?
All four sides are congruent.
Diagonals are perpendicular.
Opposite sides are parallel.
Diagonals bisect each other.
5. Prove that the quadrilateral with vertices P(-2, 1), Q(1, 3), R(6, 3), and S(3, 1) is a parallelogram. You may use any valid coordinate geometry method.