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.Construct a right-angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4·5 cm. Draw the bisector of angle PQR and let it meet PR at point T. Why is T equidistant from PQ and QR?
   • A.T lies on the angle bisector of ∠PQR, so it is equidistant from PQ and QR.
   • B.T divides PR into two equal segments, making it equidistant from PQ and QR.
   • C.T is the midpoint of PR, so it is equidistant from all sides of the triangle.
   • D.T lies on QR extended, so it is equidistant from PQ and QR.
2. 2.In what ratio is the join of the points (4, 3) and (2, -6) divided by the x-axis? Also, identify the co-ordinates of the point of intersection from the following options:
   • A.Ratio = 1 : 2, Point = (10/3, 0)
   • B.Ratio = 2 : 1, Point = (8/3, 0)
   • C.Ratio = 1 : 1, Point = (3, 0)
   • D.Ratio = 3 : 1, Point = (5/2, 0)
3. 3.Show that the points A (7, 10), B (-2, 5) and C (3, -4) are the vertices of an isosceles right-angled triangle. Which of the following correctly describes the triangle and its area?
   • A.AB = BC = √106, AB² + BC² = AC², and area = 53 square units
   • B.AB = AC = √106, AB² + AC² = BC², and area = 26.5 square units
   • C.BC = AC = √106, BC² + AC² = AB², and area = 106 square units
   • D.AB = BC = √53, AB² + BC² = AC², and area = 53 square units
4. 4.$x$-axis divides the line segment joining $A(2, -3)$ and $B(5, 6)$ in the ratio:
   • A.2:3
   • B.3:5
   • C.1:2
   • D.2:1
5. 5.Find the co-ordinates of the centroid of ΔPQR whose vertices are P (6, 3), Q (-2, 5) and R (-1, 7).
   • A.(1, 5)
   • B.(2, 5)
   • C.(1, 3)
   • D.(3, 15)