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
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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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.
See every chapter on the Geometry math page.