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.Point C(-1, 2) divides the line segment joining A(2, 5) and B(x, y) internally in the ratio 3:4. What are the values of x and y, and what is x² + y²?
   • A.x = -3, y = -4; x² + y² = 25
   • B.x = -5, y = -2; x² + y² = 29
   • C.x = 5, y = 2; x² + y² = 29
   • D.x = -4, y = -3; x² + y² = 25
2. 2.The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line $2x - y + k = 0$, find the value of $k$. Also, which of the following are the coordinates of point Q?
   • A.$k = -8$, Q = $(3, -2)$
   • B.$k = -8$, Q = $(4, -5)$
   • C.$k = 8$, Q = $(3, -5)$
   • D.$k = -4$, Q = $(4, -2)$
3. 3.Calculate the ratio in which the line y = 2 divides the segment joining A(6,5) and B(4, -3).
   • A.1:2
   • B.2:3
   • C.3:5
   • D.4:5
4. 4.The distance of a point $\mathbf{P}(x, y)$ from the origin $\mathrm{O}(0, 0)$ is given by which of the following expressions?
   • A.$$ \mathrm{OP} = \sqrt{x^2 + y^2} $$
   • B.$$ \mathrm{OP} = x + y $$
   • C.$$ \mathrm{OP} = \sqrt{x^2 - y^2} $$
   • D.$$ \mathrm{OP} = x^2 + y^2 $$
5. 5.Calculate the ratio in which the line joining the points (4, 6) and (-5, -4) is divided by the line y = 3. Also, determine the co-ordinates of the point of intersection. Which of the following correctly represents the ratio and the point of intersection?
   • A.The ratio is 3 : 7 and the point of intersection is (13/10, 3).
   • B.The ratio is 7 : 3 and the point of intersection is (-13/10, 3).
   • C.The ratio is 3 : 7 and the point of intersection is (1, 3).
   • D.The ratio is 4 : 6 and the point of intersection is (13/10, 2).