Question

Anna departs from the city A with coordinates (1, 1) towards city B with coordinates (9, 11). At the same time, Mary departs from city B towards city A. Find the coordinates of point C, where Anna and Mary meet, if b Anna is moving 3 times as fast as Mary.

Answer 1

(7, 8.5)

Explanation:

Along the x-axis, the distance is 9 - 1 = 8

Along the y-axis, the distance is 11 - 1 = 10

Since Anna travels 3 times as fast as Mary, she travels 3 times as much distance. Anna's distance is AC while Mary's distance is CB.

AC:CB = 3:1.

C is 3/(3+1) = 3/4 of AB.

Hence, the coordinate of C is

(1 + 3/4 × 8, 1 + 3/4 × 10) = (1 + 6, 1 + 7.5) = (7, 8.5)

1 is added to the components of the coordinate because A is at (1, 1).