Coordinate Proofs Worksheet
A Grade 10 Math worksheet focusing on coordinate proofs, including distance formula, midpoint formula, and slope to prove geometric properties.
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Coordinate Proofs Worksheet
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Read each question carefully and show all your work. Use the given coordinate plane for plotting points and drawing figures where indicated.
1. Find the length of the segment connecting points A(-3, 5) and B(4, -1). Show your work.
2. Determine the coordinates of the midpoint of the segment CD, where C(2, -7) and D(-6, 3). Show your work.
3. Calculate the slope of the line passing through points E(1, 8) and F(-2, -4). Show your work.
4. Given points P(1, 2), Q(4, 3), R(5, 0), and S(2, -1). Prove that PQRS is a parallelogram using the slopes of its sides.
5. Prove that the triangle with vertices J(0, 0), K(6, 0), and L(0, 8) is a right-angled triangle using coordinate geometry.
6. Which of the following statements is true about the diagonals of a rectangle in a coordinate plane?
They are perpendicular.
They bisect each other.
They are of unequal length.
They are parallel.
7. To prove that two line segments are congruent using coordinate geometry, you would use the formula.
8. If the slopes of two lines are negative reciprocals of each other, then the lines are .