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IPMAT Indore 2025 · Question 29 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 29

Let $A (1, 3)$ and $B (5, 1)$ be two points. If a line with slope $m$ intersects $A B$ at an angle of $45°$ , then the possible values of $m$ are

A $5, - \frac{1}{5}$
B $7, \frac{1}{7}$
C $3, \frac{1}{3}$
D $- 3, \frac{1}{3}$

Reveal answer

Correct answer

D.

- 3, \frac{1}{3}

Reveal solution

Slope of AB is $- 1/2$ . Using $tan 45° = ∣ (m - m_{A B}) / (1 + m \cdot m_{A B}) ∣$ , solving $∣2 m + 1∣/∣2 - m ∣ = 1$ gives $m = 1/3$ or $m = - 3$ .

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