Question

In the given figure, PQR is a right angled triangle, right angled at Q. An ant travels from P to Q, covering 13 m. Then, it travels from Q to R covering 12 m. What is the distance travelled by the ant? Also, what is its displacement from the initial position?

• A. Displacement: 25m , Distance: 25m
• B. Displacement: 25m , Distance: 5m
• C. Displacement: 5m , Distance: 25m
• D. Displacement: 5m , Distance: 5m

Answer 1

The correct option is C

Displacement: 5m , Distance: 25m

Distance is the length of path travelled.
Given, PR = 13 m and RQ = 12 m

Total Distance Travelled = PR + RQ = 13 + 12 = 25m

Displacement is shortest path between the initial and the final point.
Initial position is P and final position is Q and the shortest path is the line segment PQ.

We know that PQR is a right angled triangle.

Using pythagoras theorem,

${\text{PR}}^2={\text{PQ}}^2+{\text{QR}}^2$
Displacement = PQ = $\sqrt{{13}^2-{12}^2}$ = 5m.