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Lines and Angles Worksheets

Lines and Angles Worksheets
  • Page 1
 1.  
Find the inclination of the line y = x + 32.
a.
90o
b.
45o
c.
60o
d.
30o


Solution:

y = x + 32

Slope = m = tan θ = 1
[Compare with y = mx + c.]

θ = tan-1(1) = 45o

So, the inclination of the line is θ = 45o


Correct answer : (2)
 2.  
What is the measure of the angle between the two lines having the slopes - 7 and 1 7.
a.
45o
b.
60o
c.
30o
d.
90o


Solution:

The slopes of the lines are m1= - 7, m2 = 1 / 7.

The angle between the two lines is θ = Tan-1[-7-171-7 17] .
[Use the formula to find the angle between the two lines.]

= Tan-1()

= 90o


Correct answer : (4)
 3.  
If a non vertical line has an inclination θ with the positive x-axis, then find the slope m of the line in terms of θ.
a.
cosec θ
b.
cot θ
c.
tan θ
d.
sin θ


Solution:

If a non vertical line has an inclination θ with the positive x-axis, then the slope m of the line is given by tan θ.


Correct answer : (3)
 4.  
Find the measure of the angle between two lines having slopes 7 and 1 7 .
a.
tan-1(48)
b.
tan-1(49)
c.
tan-1(24 7)
d.
tan-1(1 14)


Solution:

The slopes of the lines are m1 = 7, m2 = 1 / 7

The angle between the two lines is θ = Tan-1[7-171+7.17] .
[Use the formula to find the angle between two lines.]

= Tan-1[(49-17)2]

= tan-1(24 / 7)


Correct answer : (3)
 5.  
Find the measure of the angle between the two lines 8x + 9y = 1 and 4x + 7y = 1.
a.
- tan-1(4 19)
b.
tan-1(1 95 )
c.
tan-1(20 )
d.
tan-1(7 )


Solution:

The two lines are 8x + 9y - 1 = 0 and 4x + 7y - 1 = 0.

y = (- 8 / 9)x + (1 / 9) and y = (- 4 / 7)x + (1 / 7)
[Convert into y = mx + c form.]

The slopes of the lines are m1 = - 8 / 9 and m2 = - 4 / 7
[Write the slopes of the two lines.]

The angle between the given lines is θ = Tan-1[-89+471+(-89)(-47)] .
[Use the formula to find the angle between the lines.]

= - tan-1(4 / 19)


Correct answer : (1)
 6.  
What is the measure of the angle between the two lines 5x + y + 4 = 0 and 5x - y - 3 = 0?
a.
tan-1(24 )
b.
- tan-1(5 12)
c.
tan-1(5 12)
d.
tan-1(10 )


Solution:

The two lines are 5x + y + 4 = 0 and 5x - y - 3 = 0.

y = - 5x - 4 and y = 5x - 3
[Convert it into y = mx + c form.]

The slopes of the two lines are m1 = - 5 and m2 = 5
[Write the slopes of the two lines.]

The angle between the given lines is θ = Tan-1[-5 - 51 - 25]
[Use the formula to find the angle between the two lines.]

= tan-1(5 / 12)


Correct answer : (3)
 7.  
What is the perpendicular distance between the point (2, 2) and the line 12x + 16y + 2 = 0.
a.
20 units
b.
120 units
c.
58 units
d.
29 10units


Solution:

The perpendicular distance between the point (2, 2) and the line 12x + 16y + 2 = 0 is d = |12(2)+16(2)+2|122+162
[The perpendicular distance from the point P (x1, y1) and the line Ax + By + C = 0 is d = |Ax1+By1+C|A2+B2.]

= 29 / 10 units


Correct answer : (4)
 8.  
What is the slope of the line on which for every point the ordinate is same?
a.
Undefined
b.
Infinitely large
c.
Infinitely small


Solution:

Let L be the line on which for every point the ordinate is same.

So, let P(14,9) and Q(19,9) be the two points on line L.

Slope of line L = Slope of line joining P,Q = m = ΔyΔx

= 9 - 919 - 14
[Use the slope formula.]

= 05 = 0


Correct answer : (2)
 9.  
The angle of inclination of a line is 3 π4. What is the slope of the line?
a.
-1
b.
1
c.
-2
d.
2


Solution:

The inclination of the line = θ = 3 π4

Slope of the line = m = tan θ
[Use the definition of slope.]

= tan 3 π4 = -1


Correct answer : (1)
 10.  
What is the slope of a line on which for every point the x coordinate is same?
a.
Infinitely small
b.
Undefined
c.
Infinitely large


Solution:

Let L be the line on which for every point the x coordinate is same.

So, let A(3, 6), B(3, 9) be two points on line L.

Slope of line L = Slope of line joining A,B = m = ΔyΔx
[Use the slope formula.]

= 9-63 - 3

= 30 = Undefined
[Division by 0 is not defined]


Correct answer : (3)

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