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.
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 ›
Q2.
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 ›
Q3.
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 ›
Q4.
Let the line $\frac{x}{4} + \frac{y}{2} = 1$ meet the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line $x + y = 1$ . Let the point P lie on the line $x + y = 1$ such that $Δ A B P$ is an isosceles triangle with $A P = B P$ . Then the distance between M' and P is
A. $\frac{7}{3}$ B. $\frac{5}{3}$ C. $\frac{2 7}{3}$ D. $\frac{2 5}{3}$
hardAsked in NIMCET 2025View solution ›