Question

An elephant standing at the junction of two straight roads represented by the equations x−y+2=0 and y−1=0 wants to reach another road whose equation is x−y−3=0. If the elephant can move in any direction and wants to cover the shortest distance to its destination road, then the equation of the path that the elephant should follow is:

Answer 1

Answer:

y = - x

Step-by-step explanation:

x - y + 2 = 0 ⇔ y = x + 2 ..... (1)

y = 1

Coordinates of an intersection of lines (1) and y - 1 = 0 are (- 1, 1)

x - y - 3 = 0 ⇔ y = x - 3 ..... (2)

Lines (1) and (2)  are parallel ( reason: $m_{1} = m_{2} =1$ )

The shorter path between (1) and (2) is a perpendicular "road" passing through (- 1, 1).

Perpendicular line has slope, which is opposite reciprocal to line (2). ⇒

$m_{3} = - 1$

y - 1 = - (x + 1) ⇔ y = - x ..... (3)