Coordinate Geometry Proofs Worksheets Grade 10

1. Prove that quadrilateral ABCD with vertices A(8, 10), B(14, 18), C(20, 10), and D(14, 2) is a rhombus using coordinate geometry.
2. Mason is analyzing a quadrilateral with vertices at P(8, 12), Q(18, 10), R(14, 0), and S(4, 2). Using the slope formula, prove whether PQRS is a parallelogram.
3. A circle is centered at point (2, -1) on the coordinate plane and passes through point (5, 3). A tangent line is drawn to the circle at point (5, 3). Determine the equation of this tangent line in slope-intercept form.

…and 4 more problems

1. Mason is a land surveyor mapping a new housing development. He marks four points on a coordinate grid to represent the corners of a proposed park: A(-7, 2), B(2, 7), C(7, -2), and D(-2, -7). Mason needs to prove that the quadrilateral formed by these points is a square by using coordinate geometry. Determine whether ABCD is a square by calculating the side lengths, the slopes of adjacent sides, and the lengths of the diagonals.
2. Charlotte is analyzing a quadrilateral on a coordinate plane with vertices at A(8, 12), B(18, 10), C(14, 0), and D(4, 2). Using the slope formula, prove whether quadrilateral ABCD is a parallelogram.
3. Isabella is analyzing a quadrilateral on a coordinate plane with vertices at W(10, 9), X(16, 15), Y(10, 21), and Z(4, 15). Prove that this quadrilateral is a rhombus using the distance formula. Then, prove that it is also a square using the slope formula.

…and 5 more problems

1. Aroha is a landscape architect designing a triangular meditation garden for a community center. She plots the garden on a coordinate grid with vertices at A(9, 12), B(21, 4), and C(15, 20). To ensure the garden is symmetrical, she needs to prove that the triangle is isosceles. Using coordinate geometry, calculate the lengths of all three sides and identify which two sides are equal. Express all lengths in simplest radical form.
2. Aroha is a landscape architect designing a new garden for a community center. She has plotted four key points on a coordinate grid to mark the corners of a new flower bed: P(9, 12), Q(21, 16), R(17, 28), and S(5, 24). She wants to prove that this quadrilateral PQRS is a parallelogram so she can order a perfectly fitting border. Using coordinate geometry, calculate the slopes of all four sides and show that opposite sides are parallel to verify the shape is a parallelogram.
3. Prove that quadrilateral PQRS with vertices P(2, 7), Q(12, 17), R(22, 7), and S(12, -3) is a rhombus using coordinate geometry.

…and 4 more problems