Class 10 Section and Mid-Point Formula Mock Test (ICSE)

Topics in Section and Mid-Point Formula

• Section formula for internal division
• Mid-point formula
• Centroid of a triangle
• Finding the ratio of division

Section and Mid-Point Formula practice questions with answers

1. Q1Multiple choice·1 mark
   If the coordinates of the vertices of a triangle are $(1, 4)$, $(3, -2)$, and $(5, 6)$, find the coordinates of its centroid.

   1. (a)$(2, 2)$
   2. (b)$(3, \frac{8}{3})$
   3. (c)$(9, 8)$
   4. (d)$(3, 3)$
   Show answer and step marks

   1. Correct option: (b) $(3, \frac{8}{3})$+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   The line segment joining the points $(-3, 2)$ and $(6, 5)$ is divided by the $y$-axis in the ratio:

   1. (a)$2:3$ internally
   2. (b)$2:1$ internally
   3. (c)$3:2$ internally
   4. (d)$1:2$ internally
   Show answer and step marks

   1. Correct option: (d) $1:2$ internally+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   Find the coordinates of the point which divides the line segment joining $(4, -3)$ and $(8, 5)$ in the ratio $3:1$ internally.

   1. (a)$(3, 7)$
   2. (b)$(5, 1)$
   3. (c)$(7, 3)$
   4. (d)$(6, 2)$
   Show answer and step marks

   1. Correct option: (c) $(7, 3)$+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   If the mid-point of the line segment joining the points $(a, 4)$ and $(2, 6)$ is $(1, 5)$, then the value of $a$ is:

   1. (a)$1$
   2. (b)$2$
   3. (c)$0$
   4. (d)$-2$
   Show answer and step marks

   1. Correct option: (c) $0$+1

   Answer: (c)

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