SME
Grade 10 Math · Problem type
The midpoint of a segment
Use this for “Find the midpoint of the segment from (−4, 3) to (8, −5)” or “M is the midpoint; find the other end.”
Chart
M
=
(
−4 + 8
2,
3 + −5
2
)
=
(2, −1)
This is an example. Type your own values to start a new problem.
(
xₘ
,
yₘ
)
=
+
2
,
+
(
)
2
Formulas
xₘ
=
x₁
+
x₂
2
2
=
−4 + 8
2
yₘ
=
y₁
+
y₂
2
−1
=
3 + (−5)
2
Assumptions
•
The midpoint M is halfway from A to B, across and up.
•
Its coordinates are the averages: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
•
Given M and one end, the other end is as far past M: x₂ = 2xₘ − x₁.
•
The ends stay within −20 and 20 on the grid.
Step-by-step
WE KNOW
x₁ = −4, y₁ = 3, x₂ = 8, y₂ = −5
FIND
x of M (xₘ), y of M (yₘ)
Step 1 · Find x of M (xₘ)
Use xₘ = (x₁ + x₂) ÷ 2
The midpoint’s x is the average of the ends’.
xₘ
=
−4 + 8
2
xₘ
=
4
2
xₘ = 2
Step 2 · Find y of M (yₘ)
Use yₘ = (y₁ + y₂) ÷ 2
The midpoint’s y is the average of the ends’.
yₘ
=
3 − 5
2
yₘ
=
−
2
2
yₘ = −1
Check
Put the numbers back in. Both sides should match.
2
=
−4 + 8
2
✓
−1
=
3 − 5
2
✓
← Previous lesson
Coordinate geometry: distance, midpoint, partitioning a segment and coordinate proofs
Next lesson →
The point that splits a segment in a ratio
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Coordinate geometry: distance, midpoint, partitioning a segment and coordinate proofs
Main lesson
The point that splits a segment in a ratio
Use this for “Find the point P on AB, A(−2, 1) and B(10, 7), with AP:PB = 1:2.”
Prove a parallelogram with slopes
Use this for “Show that A(−3, −1), B(−1, 3), C(5, 4), D(3, 0) is a parallelogram.”
Prove a right triangle with slopes
Use this for “Is the triangle A(−1, 1), B(1, 5), C(5, 3) a right triangle?”
Perimeter and area on the grid
Use this for “Find the perimeter and area of the triangle A(0, 0), B(6, 0), C(3, 4).”