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.
The number of parallelograms formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines is
A. 6B. 9C. 12D. 18
mediumAsked in MAH MCA CET 2025View solution ›
Q3.
A line perpendicular to the line segment joining the points $(1, 0)$ and $(2, 3)$ divides it in the ratio $1 : n$ . The equation of the line is
A. $3 y + x = \frac{n + 11}{n + 1}$ B. $3 y - x = \frac{n + 11}{n + 1}$ C. $3 y + x = \frac{n - 11}{n + 1}$ D. $3 y - x = \frac{n + 11}{n - 1}$
hardAsked in AMU MCA 2016View solution ›
Q4.
A line intersects lines $5 x - y - 4 = 0$ and $3 x - 4 y - 4 = 0$ at point A and B. If a point $P (1, 5)$ on the line AB is such that $A P : P B = 2 : 1$ (internally), then point A is,
A. (75/17, 307/17)B. (85/65, 114/20)C. (15/62, 225/16)D. (90/550, 46/270)
hardAsked in MAH MCA CET 2024View solution ›
Q5.
Let a, b, c, d be non-zero numbers. If the point of intersection of the lines $4 a x + 2 a y + c = 0$ and $5 b x + 2 b y + d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then
A. a + b + c + d = 0B. ad - bc = 0C. 3bc - 2ad = 0D. 3bc + 2ad = 0
mediumAsked in NIMCET 2023View solution ›
Q6.
The range of values of $θ$ in the interval $(0, π)$ such that the points $(3, 2)$ and $(cos θ, s in θ)$ lie on the same side of the line $x + y - 1 = 0$ is
A. $(0, \frac{3 π}{4})$ B. $(0, \frac{π}{2})$ C. $(0, \frac{π}{3})$ D. $(0, \frac{π}{4})$
mediumAsked in NIMCET 2023View solution ›
Q7.
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 ›
Q8.
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 ›
Q9.
The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is (2, -1). The length of the side of the triangle is
A. $\frac{3}{2}$ B. $2$ C. $\frac{2}{3}$ D. $\frac{20}{3}$
mediumAsked in NIMCET 2013View solution ›
Q10.
The area enclosed by $∣ x ∣ + ∣ y ∣ = 1$ is
A. $1$ B. $2$ C. $3$ D. $4$
easyAsked in NIMCET 2011View solution ›
Q11.
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 ›
Q12.
$A B C$ is an isosceles triangle with $A B = A C$ , and $B C$ is parallel to the x-axis. If $m_{1}$ and $m_{2}$ are the slopes of the medians drawn from $B$ and $C$ respectively, then:
A. $m_{1} m_{2} = - 1$ B. $m_{1} + m_{2} = 0$ C. $m_{1} m_{2} = 2$ D. $(m_{1} + m_{2})^{2} + 2 m_{1} m_{2} = 0$
mediumAsked in NIMCET 2009View solution ›
Q13.
A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line has intercepts $p$ and $q$ . Which of the following is true?
A. $a^{2} + b^{2} = p^{2} + q^{2}$ B. $\frac{1}{a ^{2}} + \frac{1}{b ^{2}} = \frac{1}{p ^{2}} + \frac{1}{q ^{2}}$ C. $a^{2} + p^{2} = b^{2} + q^{2}$ D. $\frac{1}{a ^{2}} + \frac{1}{q ^{2}} = \frac{1}{b ^{2}} + \frac{1}{q ^{2}}$
mediumAsked in NIMCET 2008View solution ›
Q14.
The lines $p x + q y = 1$ and $q x + p y = 1$ are respectively the sides AB and AC of a triangle ABC, and the base BC is bisected at $(p, q)$ . The equation of the median of the triangle through the vertex A is
A. $(2 pq - 1) (q x + p y - 1) - (p^{2} + q^{2} - 1) (p x + q y - 1) = 0$ B. $(2 pq - 1) (p x + q y - 1) + (p^{2} + q^{2} - 1) (q x + p y - 1) = 0$ C. $(2 pq - 1) (p x + q y - 1) - (p^{2} + q^{2} - 1) (q x + p y - 1) = 0$ D. $(2 pq - 1) (q x + p y - 1) + (p^{2} + q^{2} - 1) (p x + q y - 1) = 0$
hardAsked in NIMCET 2021View solution ›
Q15.
Let $a$ be the distance between the lines $- 2 x + y = 2$ and $2 x - y = 2$ , and $b$ be the distance between the lines $4 x - 3 y = 5$ and $6 y - 8 x = 1$ , then
A. $40 b = 115 a$ B. $402 a = 11 b$ C. $112 b = 40 a$ D. $112 a = 40 b$
mediumAsked in NIMCET 2022View solution ›
Q16.
The area of the parallelogram formed by the lines $y = 4 x$ , $y = 4 x + 1$ , $x + y = 0$ and $x + y = 1$ is
A. $\frac{1}{5}$ B. $\frac{2}{5}$ C. 5D. 10
mediumAsked in NIMCET 2022View solution ›
Q17.
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 ›
Q18.
If (2, 1), (-1, -2), (3, 3) are the mid-points of the sides BC, CA, AB of a triangle ABC, then the equation of the line BC is
A. $5 x + 4 y + 6 = 0$ B. $5 x - 4 y - 6 = 0$ C. $5 x + 4 y - 6 = 0$ D. $5 x - 4 y + 6 = 0$
mediumAsked in NIMCET 2015View solution ›
Q19.
If (-4, 5) is one vertex and $7 x - y + 8 = 0$ is one diagonal of a square, then the equation of the other diagonal is
A. $x + 7 y = 21$ B. $x + 7 y = 31$ C. $x + 7 y = 28$ D. $x + 7 y = 35$
mediumAsked in NIMCET 2015View solution ›
Q20.
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 ›

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