Question 1 :
Write the equations of
the straight lines parallel to x-axis which are at a distance of 5 units from
the x-axis
Solution :
The line which is drawn from above the x axis and parallel to the x axis will be a horizontal line.
So, the required equations will be y = 5 and y = -5.
Question 2 :
Find the equations of the straight lines parallel to the coordinates axes and passing through the point (-5, -2)
Solution :
via one point, we can draw infinite number of lines. Since the required lines will be parallel to x and y axis, we can draw two lines as follows.
Therefore the two required equations are
y = -2 and x = -5.
Question 3 :
Find the equation of a straight line whose
(i) Slope is -3 and y-intercept is 4.
Solution :
Slope (m) = -3
Y-intercept (b) = 4
Equation of the straight line:
y = mx + b
y = 3x + 4
So, the required equation of the line y = 3x+4.
(ii) Angle of inclination is 60 degree and y-intercept is 3.
Solution :
Slope (m) = tan θ
m = tan 60
m = √3
y-intercept (b) = 3
Equation of the straight line :
y = mx + b
y = √3x + 3
So, the required equation of the line y = √3x + 3.
Question 4 :
Find the equation of the line intersecting the y-axis at a distance of 3 units above the origin and
tan θ = 1/2
where Ѳ is the angle of inclination.
Solution :
The required line is intersecting the y-axis at a distance of 3 units above the origin. So we can take y-intercept as 3
tan θ = 1/2
m = 1/2
Equation of the straight line :
y = mx + b
y = (1/2)x + 3
y = (x + 6)/2
2y = x + 6
x – 2y + 6 = 0
Question 5 :
Find the equation of the straight line which passes through the midpoint of the line segment joining
(4, 2) and (3, 1)
whose angle of inclination is 30 degree.
Solution :
First we have to find midpoint of the line segment joining the points (4, 2) and (3, 1)
Midpoint = (x_{1} + x_{2})/2, (y_{1} + y_{2})/2
= (4 + 3)/2, (2 + 1)/2
= (7/2, 3/2)
angle of inclination = 30°
θ = 30°
Slope (m) = tan θ
m = tan 30°
m = 1/√3
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(y - (3/2)) = (1/√3)(x - (7/2))
(2y - 3) = (1/√3)(2x - 7)
2√3y - 3√3 = 2x - 7
2x - 2√3y - 7 + 3√3 = 0
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