Vidaara.orgClass 11 · Mathematics
CodeVID-M11-09-SLP-01
Slope & Angle Between Lines — 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 slope of a horizontal line is:
- A.$0$
- B.undefined
- C.$1$
- D.$\infty$
2.
The slope of the line through $(1,2)$ and $(3,6)$ is:
- A.$1$
- B.$2$
- C.$3$
- D.$\tfrac12$
3.
Two lines are perpendicular if:
- A.$m_1=m_2$
- B.$m_1m_2=-1$
- C.$m_1+m_2=1$
- D.$m_1m_2=1$
4.
The slope of $y=-3x+1$ is:
- A.$1$
- B.$-3$
- C.$3$
- D.$-1$
5.
The slope of a vertical line is:
- A.$0$
- B.$1$
- C.undefined
- D.$-1$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the slope of the line through $(2,3)$ and $(4,7)$.
7.
Find the slope of $2x+3y=6$.
8.
Are $y=2x+1$ and $y=2x-5$ parallel?
9.
Find the slope of a line perpendicular to $y=3x$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the angle between two lines with slopes $1$ and $0$.
11.
Find the slope of a line making $60^\circ$ with the positive x-axis.
12.
Show that $2x+3y=5$ and $3x-2y=7$ are perpendicular.
13.
Find $k$ if $y=kx$ and $y=2x+1$ are parallel.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the angle between the lines $\sqrt3\,x+y=1$ and $x+\sqrt3\,y=1$.
15.
If the points $A(1,2),\ B(3,k),\ C(5,8)$ are collinear, find $k$.
Answer Key
Section A — Multiple Choice Questions
- (A) $0$
- (B) $2$
- (B) $m_1m_2=-1$
- (B) $-3$
- (C) undefined
Section B — Short Answer (2 marks)
- $2$.
- $-\tfrac23$.
- Yes.
- $-\tfrac13$.
Section C — Short Answer (3 marks)
- $45^\circ$.
- $\sqrt3$.
- Slopes $-\tfrac23$ and $\tfrac32$; product $=-1$, so perpendicular.
- $k=2$.
Section D — Long Answer (5 marks)
- $30^\circ$.
- $k=5$.
Generated by Vidaara.org · Assignment VID-M11-09-SLP-01 · vidaara.org