Vidaara.orgClass 11 · Mathematics
CodeVID-M11-09-DIS-01
Distance of a Point from a Line — 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 distance from $(x_1,y_1)$ to $ax+by+c=0$ is:
- A.$\tfrac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}$
- B.$|ax_1+by_1+c|$
- C.$\tfrac{1}{\sqrt{a^2+b^2}}$
- D.$a+b+c$
2.
The distance from the origin to $x+y=2$ is:
- A.$2$
- B.$\sqrt2$
- C.$1$
- D.$\tfrac12$
3.
The distance between $y=2$ and $y=5$ is:
- A.$2$
- B.$3$
- C.$5$
- D.$7$
4.
The distance from $(3,4)$ to the x-axis is:
- A.$3$
- B.$4$
- C.$5$
- D.$7$
5.
The distance from $(0,0)$ to $3x+4y+5=0$ is:
- A.$1$
- B.$5$
- C.$\tfrac15$
- D.$0$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the distance from $(1,2)$ to $3x+4y-10=0$.
7.
Find the distance from the origin to $5x+12y=26$.
8.
Find the distance between $3x+4y=5$ and $3x+4y=15$.
9.
Find the distance from $(2,3)$ to the y-axis.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the distance from $(2,-1)$ to $4x+3y+1=0$.
11.
Find the distance between $3x-4y+7=0$ and $3x-4y+2=0$.
12.
Find the length of the perpendicular from $(1,1)$ to $x+y-4=0$.
13.
Find $k$ if the distance from $(1,1)$ to $3x+4y+k=0$ is $2$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the equations of the lines parallel to $3x-4y+5=0$ and at a distance of $2$ units from it.
15.
Find the distance of the point $(3,-5)$ from the line $3x-4y-26=0$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\tfrac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}$
- (B) $\sqrt2$
- (B) $3$
- (B) $4$
- (A) $1$
Section B — Short Answer (2 marks)
- $\tfrac15$.
- $2$.
- $2$.
- $2$.
Section C — Short Answer (3 marks)
- $\tfrac65$.
- $1$.
- $\sqrt2$.
- $k=3$ or $k=-17$.
Section D — Long Answer (5 marks)
- $3x-4y+15=0$ and $3x-4y-5=0$.
- $\tfrac35$.
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