The distance between streets is around $80 m$ and the distance between avenues is around $260 m$ , as shown below.

Point $X$ is at the centre of the junction of $18^{th}$ Street and $7^{th}$ Avenue.
Point $Y$ is at the centre of the junction of $24^{th}$
Street and $2^{nd}$ Avenue.
Using the information above,
a) calculate the straight-line distance between point $X$ and point $Y$ .
b) calculate the shortest distance along the roads to get from point $X$ to point $Y$ .
Give your answers to the nearest metre.

Answer

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Answer

b) $d_{r o a d} = Δ x + Δ y = 480 m + 1300 m = 1780 m$

Steps

Step 1 ： $Δ x = (24 - 18) \times 80 m = 6 \times 80 m = 480 m$

Step 2 ： $Δ y = (7 - 2) \times 260 m = 5 \times 260 m = 1300 m$

Step 3 ：a) $d_{X Y} = \sqrt{Δ x^{2} + Δ y^{2}} = \sqrt{480^{2} + 1300^{2}} \approx 1392 m$

Step 4 ：b) $d_{r o a d} = Δ x + Δ y = 480 m + 1300 m = 1780 m$