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.

Sample questions

1. 1.$ABC$ is a triangle and $G(4,3)$ is its centroid. Given $A(1,3)$, $B(4,b)$, and $C(a,1)$, what are the values of $a$ and $b$, and what is the length of side $BC$?
   • A.$a = 7$, $b = 5$, $BC = 5$ units
   • B.$a = 5$, $b = 7$, $BC = 3$ units
   • C.$a = 3$, $b = 4$, $BC = 4$ units
   • D.$a = 4$, $b = 3$, $BC = 6$ units
2. 2.Find the coordinates of the centroid of a triangle with vertices A(-1,3), B(1,-1), and C(5,1).
   • A.(1, 1)
   • B.(5/3, 1)
   • C.(2, 1)
   • D.(3, 5/3)
3. 3.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.
4. 4.Points $A(2, 2)$, $B(-2, 4)$ and $C(2, 6)$ are the vertices of a triangle $ABC$. Which of the following statements proves that $ABC$ is an isosceles triangle?
   • A.The lengths of AB and BC are both equal to $2\sqrt{5}$ units.
   • B.The length of AC is $4$ units, while AB and BC are different.
   • C.The triangle has two angles equal, making it isosceles.
   • D.The lengths of AB, BC, and AC are all equal to $2\sqrt{5}$ units.
5. 5.In what ratio does the x-axis divide the line segment joining the points (-4, -6) and (-1, 7)? Also, what are the coordinates of the point of division?
   • A.6:7, (-34/13, 0)
   • B.7:6, (-34/13, 0)
   • C.6:7, (0, -34/13)
   • D.5:6, (-34/13, 0)