1. Find the midpoint of the segment joining A(2, 4) and B(6, 8).
- A(4, 6)
- B(8, 12)
- C(2, 2)
- D(4, 4)
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Answer: A) (4, 6)
Midpoint = ((2+6)/2, (4+8)/2) = (8/2, 12/2) = (4, 6).
Class 10 Midpoint Applications — practice questions with answers
Geometry — Coordinates · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. If (5, k) is the midpoint of (2, 3) and (8, 9), then k = ?
- A6
- B12
- C5
- D7
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Answer: A) 6
k = (3 + 9)/2 = 12/2 = 6.
3. In quadrilateral ABCD the diagonals AC and BD bisect each other. A school project asks: if A(1, 2), C(7, 8), and the midpoint of BD must equal the midpoint of AC, find that common midpoint.
- A(4, 5)
- B(8, 10)
- C(3, 4)
- D(4, 4)
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Answer: A) (4, 5)
Midpoint of AC = ((1+7)/2, (2+8)/2) = (4, 5). Diagonals of a parallelogram bisect each other, so BD has the same midpoint.
4. Three collinear points lie on a line so that B is the midpoint of AC. If A(2, 5) and B(6, 9), find C.
- A(10, 13)
- B(4, 7)
- C(8, 14)
- D(10, 14)
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Answer: A) (10, 13)
C = (2*6 - 2, 2*9 - 5) = (12-2, 18-5) = (10, 13).
5. A(0, 0), B(6, 0), C(6, 8), D(0, 8) is a rectangular field. Posts are at the midpoints of AB, BC, CD, DA. A diagonal rope is tied from the midpoint of AB to the midpoint of CD. Find the length of this rope.
- A16
- B7
- C8
- D9
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Answer: C) 8
Midpoint of AB = (3, 0); midpoint of CD = (3, 8). Length = .
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