Direction: Study the given information carefully and answer the following questions. A is 20 m to the north of Z. B is 60 m to the east of Z. B is 20 m to the south of J. S is 5 m south of B. Q is 5 m to the west of A. R is 60 m to the west of S.
What is the shortest distance between A and R?
25 m
Calculating Shortest Distance in Spatial Reasoning
This problem involves determining the relative positions of different points based on the given directions and distances and then calculating the shortest distance between two specific points, A and R.
Step-by-Step Analysis of Point Positions
Let's break down the information provided to understand the layout:
- A is 20 m to the north of Z.
- B is 60 m to the east of Z.
- B is 20 m to the south of J. (This implies J is 20 m to the north of B).
- S is 5 m south of B.
- Q is 5 m to the west of A.
- R is 60 m to the west of S.
Determining Coordinates
To find the shortest distance, it's helpful to think in terms of coordinates. Let's assume Z is at the origin (0,0).
- Z: (0, 0)
- A: 20 m north of Z means A is at (0, 20).
- B: 60 m east of Z means B is at (60, 0).
- S: 5 m south of B (60, 0) means S is at (60, 0-5) = (60, -5).
- R: 60 m west of S (60, -5) means R is at (60-60, -5) = (0, -5).
We are asked to find the shortest distance between A and R.
- Point A is at (0, 20).
- Point R is at (0, -5).
Calculating the Shortest Distance
Points A and R have the same x-coordinate (0). This means they lie on a vertical line. The shortest distance between two points on a vertical line is the absolute difference of their y-coordinates.
Shortest Distance = $|y_A - y_R|$
Shortest Distance = $|20 - (-5)|$
Shortest Distance = $|20 + 5|$
Shortest Distance = $|25|$
Shortest Distance = 25 m
The calculated shortest distance between point A and point R is 25 m.
Important Questions from Direction and Distance Stops
Six houses, A, B, C, D, E and F, are situated in a colony. D is 60 m south of E. F is 40 m south of B. A is 30 m north of E. F is 50 m east of A. C is 50 m west of B. Find the location of C with reference to A.
One morning, Chitrashi and Ayaan sit facing each other. If the shadow of Ayaan falls to the left of Chitrashi, then in which direction is Ayaan facing?
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
What should come in place of the question mark (?) in the given series?
28 39 53 70 90 ?Pranay starts from Point A and drives 8 km towards east. He then takes a right turn, drives 11 km, turns right and drives 12 km. He then takes a right turn and drives 13 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
