Maths-

General

Easy

Question

# A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.

Hint:

### Use Pythagoras property.

## The correct answer is: the coffee shop at M is equidistant from each corner.

### Complete step by step solution:

Here, take one vertex A to be at origin and length of the square = 2m.

We have AE = EB = BF = FD = DG = GC = CH = HA = HM = MF= MG =ME = m

(since it is a square and H and G are midpoints of CD and AC.

Also, GE ⟂ AB and FH ⟂ AC)

By using Pythagoras property,

Length of CM =

Length of DM =

Length of AM =

Length of BM =

Hence, the coffee shop at M is equidistant from each corner.

Length of DM =

Length of BM =

Hence, the coffee shop at M is equidistant from each corner.

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