Geometry Coordinate Geometry and Proofs Test with Point Values (PDF)

Geometry math test: Coordinate Geometry and Proofs – Maths PDF

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This coordinate geometry test for Geometry covers coordinate geometry and proofs (Common Core G-GPE.B.4, G-GPE.B.5, G-GPE.B.6, G-GPE.B.7), with a free PDF to print.

This 45-minute test checks slopes, distance, partitioning segments and coordinate proofs. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Coordinate Geometry and Proofs
Standards: G-GPE.B.4, G-GPE.B.5, G-GPE.B.6, G-GPE.B.7
Time: 45 minutes
Total: 20 points

Coordinate geometry test: questions

Question 1 – Parallel and perpendicular [2 pts]

The line m passes through (2, 5) and (6, 7). (a) Write an equation of the line through (0, 1) parallel to m. (b) Write the slope of a line perpendicular to m.

Question 2 – Perpendicular through a point [2 pts]

Write an equation of the line through (3, -2) that is perpendicular to y = 3x + 4.

Question 3 – Partition and distance [3 pts]

Segment AB.

Find the point P on AB with AP : PB = 1 : 3. (1 point)
Find the length of AB in simplest radical form. (1 point)
Find the length of AP. (1 point)

Question 4 – Perimeter [2 pts]

Triangle ABC.

Find the perimeter of triangle ABC.

Question 5 – Area [2 pts]

Find the area of the triangle with vertices (1, 1), (9, 1) and (5, 7).

Question 6 – Rectangle proof [3 pts]

Quadrilateral ABCD.

Prove that the quadrilateral with vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4) is a rectangle, and find the length of its diagonals.

Question 7 – Isosceles triangle [2 pts]

Show that the triangle with vertices A(-2, 0), B(2, 0) and C(0, 6) is isosceles and find its perimeter.

Question 8 – Meeting point [2 pts]

Two friends live at (1, 2) and (13, 14) on a map grid. They meet two thirds of the way from the first friend to the second. Find the meeting point.

Question 9 – Parallelogram [2 pts]

Show that the quadrilateral with vertices A(0, 0), B(4, 1), C(6, 5) and D(2, 4) is a parallelogram by finding the midpoints of both diagonals.

Key facts behind this coordinate geometry test

Key facts

Parallel lines: equal slopes. Perpendicular lines: slopes multiply to -1.
Point P with AP:PB = a:b is a/(a+b) of the way from A to B.
Distance: square root of (x2 – x1) squared plus (y2 – y1) squared.
Perimeter = sum of distances; area uses base times height or decomposition.
Coordinate proofs test slopes (parallel, perpendicular) and distances (equal sides).

How to use this coordinate geometry test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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