Suresh walked 90 meters towards south and moves 85 meters towards East and then moves 85 meters towards North and then moves a distance of 50 meters towards West. The distance from the starting point is?
(a) 30
(b) 6√2
(c) 50√2
(d) 40√2
Answer (2)
To solve this problem, we need to determine the shortest distance from the starting point to the endpoint after Suresh's movements.
Let's break down his movements step-by-step:
Starting Point: Let's consider the starting point as the origin ( (0, 0) \
Move 90 meters South: This takes him to ( (0, -90) \
Move 85 meters East: This changes his position to ( (85, -90) \
Move 85 meters North: This brings him to ( (85, -5) \
Move 50 meters West: This results in the position ( (35, -5) \
Now, we need to find the distance from this endpoint ( 35 , − 5 ) back to the starting point ( (0, 0) \
The formula to calculate the distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by:
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2
Substituting the coordinates of the points:
d = ( 35 − 0 ) 2 + ( − 5 − 0 ) 2 d = 3 5 2 + ( − 5 ) 2 d = 1225 + 25 d = 1250
d = 5 50 d = 50 2
So, the distance from the starting point is option (c) 50\sqrt{2}.
After evaluating Suresh's movements, he ends up at the coordinates (35, -5). Using the distance formula, we find the distance from the starting point (0, 0) to be 50√2. Therefore, the correct answer is option (c) 50√2.
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