Straight Lines — Chapter Test | Class 11 IMO

Q1

Distance between parallel lines x + y = 1 and x + y = 5 is:

Distance = |5−1|/√(1²+1²)=4/√2.

Q2

Which of the following lines is perpendicular to 2x + 3y = 7?

Given slope = −2/3. Perpendicular slope = 3/2. First line has slope 3/2.

Q3

If two lines have slopes 2 and 2, then they are:

Equal slopes imply parallel lines if distinct.

Q4

The distance of point (3,4) from x-axis is:

Distance from x-axis equals absolute y-coordinate.

Q5

If the general equation Ax + By + C = 0 represents a line parallel to the y-axis, then which of the following must be true?

A line parallel to the y-axis has an undefined slope and is of the form x = k. This occurs when the coefficient of y is zero, so B = 0.

Q6

A shopkeeper marks locations on a map. The line joining (2,3) and (8,9) has slope:

Slope=(9−3)/(8−2)=1.

Q7

A light ray passing through (1, 2) reflects on the x-axis at point A. The reflected ray passes through (5, 3). Find the x-coordinate of A.

Image of (1,2) across x-axis is (1,−2). The reflected ray lies on the line joining (1,−2) and (5,3). Equation: y+2 = (5/4)(x−1) → 4y+8 = 5x−5. At x-axis, y=0 → 8 = 5x−5 → 5x=13 → x=13/5.

Q8

The line through origin making inclination 135° is:

Slope = tan135° = −1.

Q9

The straight lines x = a and y = b intersect at which of the following points?

The line x = a is vertical and all points on it have x-coordinate 'a'. The line y = b is horizontal and all points have y-coordinate 'b'. Their intersection is (a, b).

Q10

A point moves such that its perpendicular distance from the x-axis is exactly 3 times its distance from the y-axis. What is its locus?

Distance to x-axis is |y|. Distance to y-axis is |x|. Given |y| = 3|x|, which simplifies to y = 3x or y = −3x (i.e., y = ±3x).

Q11

The slope of the line passing through points (2, 3) and (6, 11) is:

m = (11−3)/(6−2) = 8/4 = 2.

Q12

A road is represented by line y = 2x + 1. Another road parallel to it passes through (0,5). Its equation is:

Parallel lines have same slope 2.

Q13

What is the condition for two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to be parallel?

Parallel lines have the same slope, so −a1/b1 = −a2/b2, which means a1/a2 = b1/b2. If they are distinct lines, the ratio must not equal c1/c2.

Q14

Which line passes through the origin?

Substituting (0,0) satisfies only 2x−y=0.

Q15

The line with x-intercept 4 and y-intercept 2 is:

x/4 + y/2 =1 ⇒ x+2y=4.