1. A triangle has vertices A(0, 0), B(4, 0) and C(4, 3). How long is the side AC?
- A
- B5
- C25
- D7
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Answer: B) 5
AC = . Writing 7 adds the legs 4 + 3 instead of using the distance formula; 25 forgets the square root.
Class 10 Classifying Shapes by Coordinates — 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. Using only distances, when are three points A, B and C collinear with B lying between A and C?
- A
- BAB BC = AC
- CAB + BC = AC
- DAB = BC = AC
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Answer: C) AB + BC = AC
If B is on segment AC, the two parts add up to the whole: AB + BC = AC. is the test for a right angle at B instead.
3. Meena has shown that a quadrilateral is a rhombus. Which single extra check proves it is a square?
- AIts diagonals bisect each other
- BIts opposite sides are equal
- CAll its sides are equal
- DIts diagonals are equal
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Answer: D) Its diagonals are equal
Every rhombus already has equal sides, equal opposite sides and diagonals that bisect each other. Only a square also has equal diagonals.
4. The points A(1, 2), B(4, y), C(x, 6) and D(3, 5), in order, are the vertices of a parallelogram. Find (x, y).
- A(2, 3)
- B(6, 1)
- C(3, 6)
- D(6, 3)
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Answer: D) (6, 3)
Midpoint of AC = midpoint of BD: (1 + x)/2 = (4 + 3)/2 gives x = 6; (2 + 6)/2 = (y + 5)/2 gives y = 3.
5. A(0, 4) and B(3, 0) are vertices of triangle ABC. C is on the x-axis (C ≠ B) and AB = AC. Find C.
- A(3, 0)
- B(−4, 0)
- C(6, 0)
- D(−3, 0)
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Answer: D) (−3, 0)
AB = . For C(x, 0): , so x = ±3. x = 3 is B itself, so C = (−3, 0). (6, 0) would make BC = AB instead.
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