Midpoint — Grade 8 Math, what it means and where it is taught
The point halfway between two others: average the x values and average the y values.
Taught in Grade 8 Math.
Where it is taught
Practise this idea
14 questions in the course bank use Midpoint, in Distance on the Coordinate Plane, Definitions, Postulates & Reasoning, How to Write a Proof, Equations of Circles, Coordinate Geometry Proofs, Accumulation & Area Under a Curve. The first 8 are below; the rest are in those units.
Problem 1
Find the midpoint of (2, 4) and (8, 10).
Worked answer
(5, 7)
x: 2 + 82 = 5
y: 4 + 102 = 7
Problem 2
Find the midpoint of (-3, 6) and (5, -2).
Worked answer
(1, 2)
x: -3 + 52 = 1
y: 6 - 22 = 2
Problem 3
The midpoint of AB is (4, 5) and A is (1, 2). Find B.
Worked answer
(7, 8)
1 + x2 = 4, so x = 7
2 + y2 = 5, so y = 8
Problem 4
The midpoint of a segment is (0, 0) and one endpoint is (-6, 8). Find the other endpoint.
Worked answer
(6, -8)
-6 + x2 = 0, so x = 6
8 + y2 = 0, so y = -8
Problem 5
M is the midpoint of PQ and PM = 9. Find PQ.
Worked answer
18
MQ = PM = 9
PQ = 9 + 9 = 18
Problem 6
M is the midpoint of PQ. PM = 4y - 3 and MQ = y + 9. Find PQ.
Worked answer
26
4y - 3 = y + 9, so y = 4
PM = 13
PQ = 26
Problem 7
Which of these is an undefined term in geometry?
- Point
- Segment
- Angle
- Midpoint
Worked answer
Point
Point, line and plane are undefined.
Segment, angle and midpoint are all defined using them.
Problem 8
M is the midpoint of AB. A is at -4 and M is at 3 on a number line. Where is B?
Worked answer
10
M - A = 3 - (-4) = 7
B = 3 + 7 = 10