ICSE Class 10 Section Formula and Mid-point — Mock Test (2027)
Free online mock test for Section Formula and Mid-point (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Section Formula and Mid-point chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Show that the points L (2a, 4a), M (2a, 6a) and N (2a + √3a, 5a) are the vertices of an equilateral triangle. Which of the following confirms this property?
- A.LM = MN = NL = 2a, proving ΔLMN is equilateral.
- B.LM = 2a, MN = 4a, NL = 2a, proving ΔLMN is isosceles.
- C.The coordinates of L, M, and N lie on a straight line, forming no triangle.
- D.LM = MN = NL = a√3, proving ΔLMN is equilateral.
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2.The line segment joining the points A $(4, -3)$ and B $(4, 2)$ is divided by the point P such that AP: AB = 2:5. Which of the following are the coordinates of P?
- A.$(4, -1)$
- B.$(4, 0)$
- C.$(4, -2)$
- D.$(4, 1)$
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3.Show that the points P $(-3, 2)$, Q $(-5, -3)$, R $(2, -3)$ and S $(4, 4)$ are the vertices of a rhombus. What is the area of the rhombus?
- A.All sides are equal and diagonals are unequal; area = 45 square units
- B.All sides are equal and diagonals are equal; area = 53 square units
- C.Opposite sides are equal and diagonals bisect at 90°; area = 36 square units
- D.All sides are equal and diagonals are equal; area = 45√2 square units
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4.Find the co-ordinates of the mid-point of the line segment joining the points A (3, -1) and B (7, 9).
- A.(5, 4)
- B.(10, 8)
- C.(4, 5)
- D.(6, 3)
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5.If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B in the ratio 3:4, find the coordinates of B.
- A.(-5, -2)
- B.(5, 2)
- C.(-2, -5)
- D.(2, 5)
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