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.The mid-point of the line segment joining $(4a, 2b - 3)$ and $(-4, 3b)$ is $(2, -2a)$. Find the values of $a$ and $b$. Which of the following pairs correctly satisfies the given condition?
   • A.$a = 2$, $b = -3$
   • B.$a = -2$, $b = 3$
   • C.$a = 1$, $b = -1$
   • D.$a = 3$, $b = -2$
2. 2.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
3. 3.Calculate the coordinates of the point P which divides the line segment joining A(-3, 3) and B(2, -7) internally in the ratio 2:3.
   • A.(-1, -3)
   • B.(1, -3)
   • C.(-3, -1)
   • D.(3, -1)
4. 4.Point $A$ lies on the line segment $XY$ joining $X(6, -6)$ and $Y(-4, -1)$ such that $\frac{XA}{XY} = \frac{2}{5}$. If $A$ also lies on the line $3x + k(y + 1) = 0$, what is the value of $k$?
   • A.1
   • B.2
   • C.3
   • D.4
5. 5.Point A $(1, -5)$ is mapped as $A'$ on reflection in the $x$-axis. Point B $(3, 2)$ is mapped as $B'$ on reflection in the origin. The coordinates of $A'$ and $B'$ are determined, and $AB'$ is calculated. What is the distance $AB'$?
   • A.5 units
   • B.√13 units
   • C.10 units
   • D.√34 units