Question

The image below shows two cities, city A and city B. Which city is furthest away from the city center located at (0,0), and how far away is that city from the city center? Each square represents 1 mile.

Answer 1

Answer: City A is the farthest away. It is approximately 6.4 miles away

Explanation:

We can use the Pythagorean Theorem to determine the distances of the two cities from the center.

a²+b²=c²

We know City A is at point (4,5) so, we can picture it as a triangle and solve for the hypotenuse to find the distance from the center.

4²+5²=c²

16+25=c²

41=c²

√41 = √c²

c≈6.4

So, City A is approximately 6.4 miles away from the center

Now, we do the same to find City B at point (-3,-5), but because we are talking about distance, we can make the numbers positive, but when we square them as either a negative or a positive, the numbers will end up the same.

3²+5²=c²

9+25=c²

34=c²

√34 = √c²

c≈5.8

So, City B is approximately 5.8 miles away from the center

Because 6.4>5.8, City A is farther away from the center.