Answer:
City A is the closest
Step-by-step explanation:
Given
City A = (-3,2)
City B = (4,8)
First, we calculate the coordinates of City C
If City C is located at the midpoint between A and B, then it's coordinates is
(x1 + x2)/2 , (y1 + y2)/2
where
x1 = x coordinate of City A = -3
x2 = x coordinate of City B = 4
y1 = y coordinate of City A = -2
y2 = y coordinate of City B = 8
So, the coordinates of City C = (-3+4)/2 , (-2+8)/2
City C = (½,6/2)
City C = (½,3)
We then calculate the distance between City C and City A
And
We also calculate the distance between City C and City B
Then we compare both results
Formulation for distance = √(x2-x1)² + (y2-y1)²
For City C and City A
City A coordinatates = (x1,y1) = (-3,2)
City C coordinates = (x2,y2) = (½,3)
Distance between A and C = √(½-(-3))² + (3-2)² -------- Simplify the bracket
Distance = √(½+3)² + (1)² ---------- Solve the fraction
Distance = √(7/2)² + (1)² ------------ Open all brackets
Distance = √49/4 + 1
Distance = √53/4
Distance = 7.280109889280518/2
Distance = 3.640054944640259
Distance between City A and C = 3.64 (approximated)
For City C and City B
City B coordinatates = (x1,y1) = (4,8)
City C coordinates = (x2,y2) = (½,3)
Distance between B and C = √(½-(-3))² + (8-4)² -------- Simplify the bracket
Distance = √(½+3)² + (4)² ---------- Solve the fraction
Distance = √(7/2)² + (4)² ------------ Open all brackets
Distance = √49/4 + 16
Distance = √113/4
Distance = 10.63014581273464/2
Distance = 5.315072906367324
Distance between City B and C = 5.32 (approximated)
Comparing the results (3.64) and (5.32),
We conclude that City C is closer to City A than City B
