Geometry Unit 7: Coordinate Geometry

Distance, midpoint and partitioning a segment, slopes of parallel and perpendicular lines, and classifying figures with coordinates. 12 questions. Have a go at each one on paper before you tap "Show me how".

A free account opens the worked solutions to 20 questions a day; Pro opens every one.

Question 1

DistanceNo calculator

Points $A(-3,4)$ and $B(5,-2)$ are plotted on a grid. How long is $\overline{AB}$?

1. $2\sqrt{7}$
2. $14$
3. $100$
4. $10$

Question 2

MidpointNo calculator

What is the midpoint of the segment from $(-3,7)$ to $(5,-1)$?

1. $(1,3)$
2. $(-4,4)$
3. $(2,6)$
4. $(4,-4)$

Question 3

MidpointNo calculator

$M(2,-1)$ is the midpoint of $\overline{AB}$, and $A$ is $(-4,3)$. Where is $B$?

1. $(-10,7)$
2. $(-1,1)$
3. $(8,-5)$
4. $(6,-4)$

Question 4

Partitioning a segmentNo calculator

Point $P$ lies on $\overline{AB}$, one third of the way from $A(-1,2)$ to $B(8,14)$. Where is $P$?

1. $(-4,-2)$
2. $(2,6)$
3. $(3.5,8)$
4. $(5,10)$

Question 5

Perpendicular slopesNo calculator

What is the slope of a line perpendicular to the line through $(-2,1)$ and $(4,-3)$?

1. $-\frac{3}{2}$
2. $-\frac{2}{3}$
3. $\frac{3}{2}$
4. $\frac{2}{3}$

Question 6

Classifying quadrilateralsNo calculator

A quadrilateral has vertices $(0,0)$, $(4,0)$, $(5,3)$ and $(1,3)$, in order. What is the most specific name for it?

1. Square
2. Rectangle
3. Parallelogram
4. Rhombus

Question 7

Perimeter on the planeNo calculator

What is the perimeter of the triangle with vertices $(0,0)$, $(6,0)$ and $(6,8)$?

1. $48$
2. $20$
3. $14$
4. $24$

Question 8

Area on the planeNo calculator

What is the area of the triangle with vertices $(1,1)$, $(7,1)$ and $(4,6)$?

1. $30$
2. $18$
3. $12$
4. $15$

Question 9

Perpendicular bisectorsNo calculator

Which is the equation of the perpendicular bisector of the segment from $(2,4)$ to $(6,8)$?

1. $y=-x+6$
2. $y=x+2$
3. $y=x-2$
4. $y=-x+10$

Question 10

Right triangles on the planeNo calculator

Triangle $ABC$ has vertices $A(1,1)$, $B(4,5)$ and $C(8,2)$. Where is its right angle?

1. At C
2. At A
3. It has no right angle
4. At B

Question 11

DistanceCalculator

What is the distance between $(-1,4)$ and $(5,-3)$, to the nearest tenth?

1. $13.0$
2. $9.2$
3. $9.3$
4. $8.5$

Question 12

Circles on the planeNo calculator

A diameter of a circle has endpoints $(-2,5)$ and $(6,-1)$. What is the radius?

1. $5$
2. $25$
3. $5\sqrt{2}$
4. $10$