Vidaara.orgClass 10 · Mathematics
CodeVID-M10-06-SEC-01
Section Formula — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The internal section formula for $x$ is:
- A.$\tfrac{mx_2+nx_1}{m+n}$
- B.$\tfrac{x_1+x_2}{2}$
- C.$mx_1+nx_2$
- D.$\tfrac{mx_1-nx_2}{m-n}$
2.
The midpoint formula gives:
- A.$\left(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2}\right)$
- B.$(x_1+x_2,y_1+y_2)$
- C.$(x_1x_2,y_1y_2)$
- D.$(0,0)$
3.
The midpoint of $(2,4)$ and $(6,8)$ is:
- A.$(4,6)$
- B.$(8,12)$
- C.$(3,6)$
- D.$(2,2)$
4.
The point dividing $(0,0)$ and $(4,8)$ in $1:1$ is:
- A.$(2,4)$
- B.$(4,8)$
- C.$(1,2)$
- D.$(0,0)$
5.
A midpoint divides a segment in the ratio:
- A.$1:2$
- B.$1:1$
- C.$2:3$
- D.$3:1$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the midpoint of $(1,2)$ and $(5,6)$.
7.
Find the point dividing $(1,2)$ and $(7,8)$ in the ratio $1:2$.
8.
Find the midpoint of $(-2,3)$ and $(4,-1)$.
9.
Find the point dividing $(2,3)$ and $(6,7)$ in the ratio $3:1$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the point dividing $(4,-3)$ and $(8,5)$ in the ratio $3:1$.
11.
In what ratio does $(-4,6)$ divide the segment joining $(-6,10)$ and $(3,-8)$?
12.
A circle's diameter has endpoints $(3,4)$ and $(-1,2)$; find its centre.
13.
The midpoint of $(a,b)$ and $(c,d)$ is $(3,4)$. If $(a,b)=(1,2)$, find $(c,d)$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the ratio in which the line $2x+y-4=0$ divides the segment joining $A(2,-2)$ and $B(3,7)$.
15.
Find the coordinates of the points of trisection of the segment joining $(4,-1)$ and $(-2,-3)$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\tfrac{mx_2+nx_1}{m+n}$
- (A) $\left(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2}\right)$
- (A) $(4,6)$
- (A) $(2,4)$
- (B) $1:1$
Section B — Short Answer (2 marks)
- $(3,4)$.
- $(3,4)$.
- $(1,1)$.
- $(5,6)$.
Section C — Short Answer (3 marks)
- $(7,3)$.
- $2:7$.
- $(1,3)$.
- $(5,6)$.
Section D — Long Answer (5 marks)
- $2:9$.
- $\left(2,-\tfrac53\right)$ and $\left(0,-\tfrac73\right)$.
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