Playbook
Straight Line
43 q - 0.96/paper - 19% HARD. Four notes pages of routine coordinate geometry; every HARD question sits on the slope-and-angle page (15 q, 33%), and the distance page shares its whole toolkit with Line and Plane, so it costs almost nothing on top of a cornerstone you already own.
- Questions in the bank
- 43
- q/paper (2024–25 shifts)
- 0.96
- Tagged HARD
- 19%
- Subtopics
- 4
Strand: Quick-Win
When you’ll see it
A line in the plane: a point dividing a segment, a distance from a point, three lines tested for concurrency, an angle between two lines, or a bisector.
How this chapter is tested
43 q at 0.96 per paper and 20% HARD. Four notes pages (/notes/mht-cet-maths/straight-line), all routine coordinate geometry, and the reason this sits in the Quick-Win strand rather than the long tail is not its size — it is that it shares its whole toolkit with Line and Plane, a cornerstone worth 4.96 questions a paper. Section formula, foot of perpendicular, distance from a point, angle between two objects: every one of these is the 2-D version of a move you already have to own.
Slope, Angle Between Lines and Rotation is 15 q at 33% HARD and holds every HARD question in the chapter: lines through a point at a given angle, a rotation about a point, the bisector at a vertex, a reflected slope — all the angle formula solved for the unknown slope. Forms, Intersections and Concurrency (13 q, 15%), Distance (9 q, 11%) and the Section Formula page (6 q, 0%) are cheap.
One idea in here pays well beyond this chapter. Concurrency of three lines is a vanishing 3x3 determinant, and the survey found that same determinant working as a universal degeneracy test across five or six chapters — as collinearity of three points, as coplanarity of lines in three dimensions, and as scalar triple product zero in Vectors. Learn the test once and recognise its four costumes.
The same is true of the angle condition. The survey counted the angle-between-two-objects idea across 87 q in 7 chapters and perpendicularity across 83 q in 7. Here it is the slope-product condition; in Vectors it is a dot product; in Pair of Straight Lines it is a coefficient sum. One idea, four dialects.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Slope, Angle Between Lines and Rotation
Slope from two points or from ax + by + c = 0, parallel and perpendicular conditions, tan θ = |(m1 − m2)/(1 + m1m2)|, the two lines through a point at a given angle, rotation about a point, and the bisector at a vertex. 15 q at 33% HARD — the whole difficulty of the chapter.
Forms of a Line, Intersections and Concurrency
Intercept form with the triangle-area and 1/a² + 1/b² = 1/p² stems, normal form, point-slope for medians and parallels, the intersection point and a line through it, and the concurrency determinant. 13 q at 15% HARD.
Section Formula, Midpoints and Rectangles
Internal and external division, the ratio in which the origin divides a segment between parallel lines, rectangle centres and missing vertices, and the circumcentre. 6 q at 0% HARD.
Distance — From a Point, Between Parallels, Along a Direction and the Foot of the Perpendicular
|ax0 + by0 + c|/√(a² + b²), the gap between parallels and the square it bounds, the foot of the perpendicular, and distance measured along a direction. 9 q at 11% HARD — directly transferable to Line and Plane.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Perpendicularity applied to a vertical line
The slope-product condition needs both slopes to exist. A line parallel to the y-axis has no slope, and the formula silently produces a wrong answer rather than failing.
The other angle bisector
Two lines have two bisectors, at right angles to each other, and both appear in the options. The question usually specifies the one containing the origin or the acute one — read which.
Distance formula without the modulus
The point-to-line distance is a non-negative quantity. The signed value, which the algebra produces first, is offered as a distractor and is the negative of the right answer.
Concurrency claimed for parallel lines
A vanishing determinant is necessary but does not by itself place three lines through one point — a set of parallel or coincident lines can satisfy it. Check that the lines actually meet.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Straight Line notesDrill every straight line question
43 questions from the bank, scoped to 4 bundled subtopics.
Drill one subtopic at a time
The 4 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.