Problem
The distance between streets is around \( 80 \mathrm{~m} \) and the distance between avenues is around \( 260 \mathrm{~m} \), as shown below. Point \( X \) is at the centre of the junction of \( 18^{\text {th }} \) Street and \( 7^{\text {th }} \) Avenue. Point \( Y \) is at the centre of the junction of \( 24^{\text {th }} \) Street and \( 2^{\text {nd }} \) 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.
Solution
Step 1 ：\(\Delta x = (24 - 18) \times 80 \mathrm{~m} = 6 \times 80 \mathrm{~m} = 480 \mathrm{~m} \)
Step 2 ：\(\Delta y = (7 - 2) \times 260 \mathrm{~m} = 5 \times 260 \mathrm{~m} = 1300 \mathrm{~m}\)
Step 3 ：a) \(d_{XY} = \sqrt{\Delta x^2 + \Delta y^2} = \sqrt{480^2 + 1300^2} \approx 1392 \mathrm{~m}\)
Step 4 ：b) \(d_{road} = \Delta x + \Delta y = 480\mathrm{~m} + 1300 \mathrm{~m} = 1780 \mathrm{~m}\)
