Example 1 · level 1
Find the midpoint of the segment joining (5, 2) and (−11, 0).
- (−16, −2)
- (−3, 1)
- (1, −3)
- (−3, −1)
Show solution
- x = (5 + (−11)) ÷ 2 = −3.
- y = (2 + 0) ÷ 2 = 1.
- Midpoint = (−3, 1).
Answer: (−3, 1)
CLASS 10 MATHS · COORDINATE GEOMETRY
Midpoint formula
The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).
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Worked examples
Example 2 · level 2
M(−5, −5) is the midpoint of AB, where A is (−7, −4). Find B.
- (−3, −6)
- (−6, −5)
- (−17, −14)
- (2, −1)
Show solution
- x = 2 × (−5) − (−7) = −3.
- y = 2 × (−5) − (−4) = −6.
- B = (−3, −6).
Answer: (−3, −6)
Example 3 · level 3
(−6, 0) is the midpoint of the segment joining (−5, −6) and (k, 6). Find k.
Show solution
- (−5 + k) ÷ 2 = −6
- −5 + k = −12
- k = −7.
Answer: -7