Geometry Coordinate Quiz with Answers – Free PDF

Contents

This geometry coordinate quiz asks 10 multiple-choice questions on coordinate geometry proofs, and each answer comes with a short explanation.

This 10-question quiz checks the core coordinate geometry skills: distance, midpoint, slopes of parallel and perpendicular lines, partitioning a segment, area, perimeter and proof criteria. Choose the one best answer for each question.

GeometryCommon Core: G-GPE.B.4 · G-GPE.B.5 · G-GPE.B.6 · G-GPE.B.7

🎯 Coordinate Geometry Proofs – Geometry math quiz

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Question 1

What is the distance between \((-1,2)\) and \((5,10)\)?

A \(10\)

B \(14\)

C \(100\)

D \(\sqrt{14}\)

Question 2

What is the midpoint of the segment with endpoints \((-6,4)\) and \((2,-10)\)?

A \((-2,-3)\)

B \((4,-7)\)

C \((-8,-6)\)

D \((-2,3)\)

Question 3

Line \(p\) passes through the two labeled points. What is the slope of a line perpendicular to \(p\)?

Line p.

A \(\frac{4}{3}\)

B \(-\frac{3}{4}\)

C \(\frac{3}{4}\)

D \(-\frac{4}{3}\)

Question 4

Which line is parallel to \(y=-2x+7\) and passes through \((1,4)\)?

A \(y=2x+2\)

B \(y=-2x+6\)

C \(y=\frac{1}{2}x+\frac{7}{2}\)

D \(y=-2x+7\)

Question 5

Point \(P\) partitions \(\overline{AB}\) in the ratio \(1:3\) measured from \(A\). What are the coordinates of \(P\)?

Segment AB.

A \((0,2)\)

B \((2,3)\)

C \((4,4)\)

D \(\left(\frac{2}{3},\frac{7}{3}\right)\)

Question 6

What is the area of the triangle shown?

Triangle on a grid.

A \(48\)

B \(28\)

C \(24\)

D \(14\)

Question 7

Which fact is enough to prove that a quadrilateral is a parallelogram?

A The diagonals have equal lengths

B One pair of opposite sides has equal length

C Both pairs of opposite sides have equal slopes

D Two adjacent sides are perpendicular

Question 8

The midpoint of \(\overline{AB}\) is \((3,-2)\) and \(A=(-1,4)\). What are the coordinates of \(B\)?

A \((1,1)\)

B \((7,-8)\)

C \((5,-6)\)

D \((-5,10)\)

Question 9

What is the perimeter of the triangle shown?

Triangle on a grid.

A \(7\)

B \(6\)

C \(7+\sqrt{7}\)

D \(12\)

Question 10

Two sides of a triangle have slopes \(\frac{2}{5}\) and \(-\frac{5}{2}\). What do the slopes show about the angle between them?

A It is an acute angle

B It is a right angle

C The sides are parallel

D It cannot be determined

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Distance: \(d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}\); midpoint: the average of the coordinates.
Parallel lines have equal slopes; perpendicular lines have slopes with product \(-1\).
A point that splits a segment in ratio \(a:b\) is \(\frac{a}{a+b}\) of the way from the first endpoint.
Perimeter adds distance-formula lengths; triangle area is \(\frac{1}{2}bh\) with a horizontal or vertical base.
A parallelogram has diagonals with the same midpoint; add a right angle to get a rectangle.