# NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 13

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1. A person standing at the junction (crossing) of two straight paths represented by the equations wants to reach the path whose equation is in the least time. Find equation of the path that he should follow.

Answer:

The equations of the given lines are

…………………. eq (1)

………………… eq (2)

……………….… eq (3)

The person is standing at the junction of the paths represented by lines (1) and (2).

On solving equations (1) and (2),

.

So, the person is standing at point

The person can reach path (3) in the least time if he walks along the perpendicular line to (3) from point .

Slope of the line

Slope of the line perpendicular to line (3)

The equation of the line passing through and having a slope of is given by

So, the path that the person should follow is .