Straight Line Questions with Solutions

25 questions9 easy12 medium4 hard

The straight line is the most fundamental topic in coordinate geometry. It covers the slope of a line, the angle between two lines, conditions for parallel and perpendicular lines, and the different forms of the equation of a line: slope-intercept, point-slope, two-point, intercept and normal forms. Exam questions also test the perpendicular distance of a point from a line, the distance between two parallel lines, the point of intersection of two lines, concurrency of three lines, and families of lines passing through an intersection point. Remember that two lines are perpendicular when the product of their slopes is -1 and parallel when their slopes are equal. Picking the right form of the equation for the information given is the main skill. Practise the straight line questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
Let $(x_{0}, y_{0}) \in Z^{2}$ be a point on the straight line $8 x - 3 y = 11$ which is equidistant from the coordinate axes. Then the point $(x_{0}, y_{0})$ will lie only in:
A. I quadrantB. II quadrantC. III quadrantD. IV quadrant
easyAsked in NIMCET 2026View solution ›
Q2.
If the straight line $a x + b y + c = 0$ always passes through $(1, - 2)$ , then a, b, c are in
A. APB. HPC. GPD. None of these
easyAsked in NIMCET 2013View solution ›
Q3.
The equation of the line parallel to the line $2 x - 3 y = 7$ and passing through the middle point of the line segment joining the points (1, 3) and (1, -7) is
A. $2 x - 3 y - 4 = 0$ B. $2 x - 3 y + 4 = 0$ C. $2 x - 3 y - 8 = 0$ D. $2 x - 3 y + 8 = 0$
easyAsked in NIMCET 2013View solution ›
Q4.
The area enclosed by $∣ x ∣ + ∣ y ∣ = 1$ is
A. $1$ B. $2$ C. $3$ D. $4$
easyAsked in NIMCET 2011View solution ›
Q5.
The distance between the parallel lines $y = 2 x + 4$ and $6 x = 3 y + 5$ is
A. $\frac{17}{3}$ B. $1$ C. $\frac{3}{5}$ D. $\frac{17 5}{15}$
easyAsked in NIMCET 2010View solution ›
Q6.
The foot of the perpendicular from the point (2, 4) upon $x + y = 1$ is
A. $(\frac{1}{2}, \frac{3}{2})$ B. $(- \frac{1}{2}, \frac{3}{2})$ C. $(\frac{4}{3}, \frac{1}{2})$ D. $(\frac{4}{3}, - \frac{1}{2})$
easyAsked in NIMCET 2015View solution ›
Q7.
If non-zero numbers a, b, c are in A.P., then the straight line $a x + b y + c = 0$ always passes through a fixed point. The point is
A. (1, -2)B. (1, -1/2)C. (-1, 2)D. (-1, -2)
easyAsked in NIMCET 2017View solution ›
Q8.
The equation of the line perpendicular to $x - 2 y = 1$ and passing through $(1, 1)$ is
A. $x + 2 y = 2$ B. $x + y = 2$ C. $y = 2 x + 3$ D. $y = - 2 x + 3$
easyAsked in NIMCET 2018View solution ›
Q9.
The obtuse angle between the lines $2 y = x + 1$ and $y = 3 x + 2$ is
A. $\frac{4 π}{5}$ B. $\frac{2 π}{3}$ C. $\frac{5 π}{6}$ D. $\frac{3 π}{4}$
easyAsked in NIMCET 2025View solution ›