A coordinate grid is placed over a map. City A is located at (- 3, 2) , and City B is located at (4, 8) . If City C is at the midpoint between City A and City B, which is closest to the distance in coordinate units from City A to City C?

Answer:City A is the closestStep-by-step explanation:GivenCity A = (-3,2)City B = (4,8)First, we calculate the coordinates of City CIf City C is located at the midpoint between A and B, then it's coordinates is(x1 + x2)/2 , (y1 + y2)/2where x1 = x coordinate of City A = -3x2 = x coordinate of City B = 4y1 = y coordinate of City A = -2y2 = y coordinate of City B = 8So, the coordinates of City C = (-3+4)/2 , (-2+8)/2City C = (½,6/2)City C = (½,3)We then calculate the distance between City C and City AAnd We also calculate the distance between City C and City BThen we compare both resultsFormulation for distance = √(x2-x1)² + (y2-y1)²For City C and City ACity 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 bracketDistance = √(½+3)² + (1)² ---------- Solve the fractionDistance = √(7/2)² + (1)² ------------ Open all bracketsDistance = √49/4 + 1Distance = √53/4Distance = 7.280109889280518/2Distance = 3.640054944640259Distance between City A and C = 3.64 (approximated)For City C and City BCity 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 bracketDistance = √(½+3)² + (4)² ---------- Solve the fractionDistance = √(7/2)² + (4)² ------------ Open all bracketsDistance = √49/4 + 16Distance = √113/4Distance = 10.63014581273464/2Distance = 5.315072906367324Distance 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