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A hospital helipad is at H(2, 2). Four ambulance posts stand at A(5, 6), B(-2, 5), C(6, -1) and D(7, 2), all distances in kilometres.
What is special about the four posts?

Class 10Distance FormulaGeometry — Coordinates
  • APost D is the nearest and post B the farthest from the helipad
  • BThey lie on a single straight line through H
  • CAll four are exactly 5 km from H, so they lie on a circle of radius 5 centred at H
  • DOnly A and D are the same distance from H

Step-by-Step Solution

and HD = |7 - 2| = 5. Every post is 5 km away, so all four lie on the circle of radius 5 km centred at , and no post is nearer than another. The negative coordinates in and do not shorten those distances, because the differences are squared.
Answer: C) All four are exactly 5 km from H, so they lie on a circle of radius 5 centred at H

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