I don’t understand stand this question someone please help me with work shown

8.9 miles

Step-by-step explanation:

well, you got 2 points with their coordinates on the grid if the city. to make it easy, the origin = point (0,0) is also the center of the city.

the school is 4 miles east = 4 units plus to the right in positive x direction.

and 2 miles south = 2 units down in negative y direction.

so, the point school is (4, -2).

the pool is 8 miles east = 8 units plus to the right in positive x direction.

and it is 6 miles north = 6 units up in positive y direction.

so, the point pool is (8, 6).

now we need to find the distance between both points to see how far they need to travel.

just one remark : this is flawed, as we can usually not make a beeline in a city from one place to another. we have to go along streets. but let's ignore that and just find the air distance.

now, to find the direct distance between 2 points, we need Pythagoras for right-angled triangles

c² = a² + b²

c = the Hypotenuse, the baseline opposite of the 90 degree angle. = the direct distance between the 2 points.

a and b are the sides of a right-angled triangle, which are nothing else than the differences of the x and y coordinates of the 2 points.

the x difference between school and pool is 8-4 = 4.

the y difference between school and pool is 6 - -2 = 6 + 2 = 8.

don't worry, if you did it the other way around and got negative numbers. remember that in the Pythagoras formula everything has to be squared first (and that turns also negative numbers into positive ones).

so, we get

c² = 4² + 8² = 16 + 64 = 80

c (the distance) = sqrt(80)

"sqrt" is the usual abbreviation of "square root".

sqrt(80) ≈ 8.9 miles

add a pic of the graph, then ill edit this "answer" and solve it for you : 3

step-by-step explanation: