Straight Lines MCQ

Ans. The correct answer is c. -3

Explanation: The given equation is

y = -3x + 2

Comparing the given equation with the equation of the straight line i.e.

y = mx + c

Where m is the slope of the straight line.

We get, slope, m = -3

Ans. The correct answer is b. 0

Explanation: Two lines are considered to be parallel if their slopes are equal. If m1 and m2 are the slopes of two parallel lines, then m₁ = m₂

⇒ m₁ - m₂ = 0

Ans. The correct answer is d. 13 units

Explanation: Since the distance of the coordinate (5, 12) is taken from the origin, then the coordinates of the origin are (0, 0).

Therefore, 

x₁ = 0, y₁ = 0

x₂ = 5, y₂ = 12

The distance between two points = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(5 - 0)² + (12 - 0)²] = 13 units

Ans. The correct answer is a. -1

Explanation: If two lines are perpendicular, then the product of their slopes will be -1.

Ans. The correct answer is c. \(-\frac{a}{b}\)

Explanation: The general equation of a straight line is given by 

ax + by + c = 0

On rearranging the equation, we get

by = - ax - c

⇒ y = \(\frac{(- ax - c)}{b}\)

⇒ y = \((-\frac{a}{b})x -(\frac{c}{b})\)

Comparing the above equation with the equation of straight-line 

y = mx + c

We get

Slope, m = \(-\frac{a}{b}\)

Ans. The correct answer is c. 2x + y – 7 = 0

Explanation: The equation of a straight line passing through two points (x₁, y₁) and (x₂ y₂) is given by

\(\frac{(y - y_1)}{(x - x_1)} = \frac{(y_2 - y_1)}{(x_2 - x_1)}\)

We have

x₁ = 1, y₁ = 5

x₂ = 2, y₂ = 3

On substituting the values, we get

(y - 5)/(x - 1) = (3 - 5)/(2 - 1)

⇒ (y - 5)/(x - 1) = (-2)/(1)

⇒ y - 5 = -2(x - 1)

⇒ y - 5 = - 2x + 2

⇒ 2x + y - 7 = 0

Therefore, the equation of a line is 2x + y - 7 = 0.

Ans. The correct answer is d. 2x - 3y + 6 = 0

Explanation: The equation of a straight line perpendicular to the line 3x + 2y + 5 = 0 is given by

2x - 3y + λ = 0

Given that this line is passing through the points (3, 4).

On substituting the values, we get

2(2) - 3(4) + λ = 0

⇒ λ = 6

On substituting λ = 6 in the above equation, we get

2x - 3y + 6 = 0

Ans. The correct answer is b. 3/10

Explanation: The equation of the first line is 3x + 4y = 9

Its slope is given by -3/4

The equation of the second line is 6x + 8y = 15

⇒ 3x + 4y = 15/2

Its slope is given by -3/4

Since slopes are equal, the lines are parallel.

Therefore, the distance between two lines is given by

D = |(c₁ – c₂)|/√(a² + b²)

On substituting the values, we get

⇒ D = |(9 – (15/2))|/√(32 + 42)

⇒ D = = 3/10

Ans. The correct answer is a. θ is an obtuse angle

Explanation: When measured anti-clockwise, the line with a negative slope forms an obtuse angle with a positive x-axis.

Ans. The correct answer is c. x - y = 0

Explanation: Let (x, y) be the abscissa and ordinate of a point P.

Given, Abscissa = Ordinate, therefore x = y

Hence, the locus of the point is x - y = 0.

Ans. The correct answer is a. True

Explanation: If the area of a triangle formed by three points is 0, the three points must be collinear, or lie on the same line.

Ans. The correct answer is a. positive y-axis

Explanation: The inclination of a line is always measured with a positive x-axis in an anticlockwise direction.

Ans. The correct answer is b. tanα

Explanation: tanα gives the slope of a line if the inclination of the line is α. The slope is represented by the tangent of the inclination angle.

Ans. The correct answer is c. 0°

Explanation: If a line is parallel to the x-axis, the angle it forms with the x-axis is zero. Therefore, its inclination is zero.

Ans. The correct answer is a. 15.29 units

Explanation: Since the distance of the coordinate (3, 15) is taken from the origin, then the coordinates of the origin are (0, 0).

Therefore, 

x₁ = 0, y₁ = 0

x₂ = 3, y₂ = 15

The distance between two points = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (15 - 0)²] = 15.29 units