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Taya2010 [7]
3 years ago
10

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 mi

dpoint between City A and City B, which is closest to the distance in coordinate units from City A to City C?
Mathematics
1 answer:
Andreyy893 years ago
7 0

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

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