JEE Maths›Straight Lines›Common Mistakes
Common Mistakes

Traps in Straight Lines

5 mistake patterns students fall for. 2 high-frequency traps appear in almost every exam.

Forgetting absolute value in distance formula

Very CommonSIGN ERROR

Distance is always positive. The formula d=∣ax1+by1+c∣a2+b2d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}} needs the absolute value.

Why: The signed version is useful for same/opposite side checks, but distance must always be positive.

WRONG: d=ax1+by1+ca2+b2d = \frac{ax_1 + by_1 + c}{\sqrt{a^2 + b^2}} without absolute value, getting negative distance
RIGHT: Always take ∣ax1+by1+c∣|ax_1 + by_1 + c|. The signed version is only for side-of-line checks.
See pattern: Distance & Position Problems →

Perpendicular slope: forgetting negative reciprocal

Very CommonSIGN ERROR

If slope of a line is mm, the perpendicular slope is −1/m-1/m, not 1/m1/m.

Why: Students remember 'reciprocal' but forget the negative sign. Product of perpendicular slopes =−1= -1.

WRONG: Perpendicular to y=2xy = 2x has slope 12\frac{1}{2}
RIGHT: Perpendicular to y=2xy = 2x has slope −12-\frac{1}{2}. Product of perpendicular slopes =−1= -1.
See pattern: Angle Between Lines / Rotation →

Confusing centroid, circumcenter, and orthocenter

CommonCONCEPT

These are different points. Centroid divides medians 2:12:1. Orthocenter is intersection of altitudes.

Why: All three are 'special points' of a triangle, and their formulas look similar.

WRONG: Using centroid formula when orthocenter is asked
RIGHT: Centroid =(x1+x2+x33,y1+y2+y33)= \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right). For orthocenter, find intersection of any two altitudes.

Section formula: internal vs external division

CommonFORMULA

Internal division uses ++ in denominator. External uses −- (or negative ratio).

Why: The formulas differ only by a sign, making it easy to apply the wrong one.

WRONG: Using internal division formula for external division
RIGHT: External division in ratio m:nm:n means use ratio m:(−n)m:(-n) in the formula, or change signs in denominator.

Angle with x-axis vs angle between two lines

CommonCONCEPT

tan⁡θ\tan\theta for angle with x-axis is just the slope. Angle between two lines uses the formula with both slopes.

Why: Both involve tan⁡\tan and slopes, but they are different geometric quantities.

WRONG: Using angle-between-lines formula when only the inclination is needed
RIGHT: Inclination: θ=arctan⁡(m)\theta = \arctan(m). Between lines: tan⁡α=∣m1−m21+m1m2∣\tan\alpha = \left|\frac{m_1 - m_2}{1 + m_1 m_2}\right|. These are different angles.
See pattern: Angle Between Lines / Rotation →
Test yourself

Can you spot these traps under time pressure?

Take a timed quiz on Straight Lines and see if you avoid the mistakes above.

→
←
Previous
Probability
Next
Definite & Indefinite Integrals
→