Question

Mary is traveling to Ecuador for her summer vacation. She looks at a map of the path of her flight. Her plane leaves from Florida, located at (5, 16) on the map’s coordinate grid, makes a stop at the halfway point, Panama, located at (6, 12) on her map’s coordinate grid. She then heads to her destination, Ecuador. Find the location of Ecuador on Mary’s map.

Answer 1

The coordinates of Ecuador is (7,8)

Explanation:

Represent Ecuador with E, Panama with P and Florida with F

Given

F(x1,y1) = (5,16)

P(x,y) = (6,12)

Required

Determine the coordinates of E(x2,y2)

From the question, we understand that P is located at the midpoint of E and F.

Using midpoint formula, we have

(x,y) = (½(x1 + x2), ½(y1 + y2))

Substitute values for x,y,x1 and y2;

This gives

(6,12) = (½(5 + x2), ½(16 + y2))

By direct comparison of expression on both sides

½(5 + x2) = 6

½(16 + y2) = 12

Solving for the first equation

Multiply both sides by 2

5 + x2 = 6 * 2

5 + x2 = 12

Make x2 the subject of formula

x2 = 12 - 5

x2 = 7

Solving the second equation

Multiply both sides by 2

16 + y2 = 12 * 2

16 + y2 = 24

Make y2 the subject of formula

y2 = 24 - 16

y2 = 8

Hence, the coordinate of Ecuador is (7,8)