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 they are moving at the same speed

Answer 1

Given:

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.

To find:

The coordinates of point C, where Anna and Mary meet, if they are moving at the same speed.

Solution:

They are moving at the same speed at the same time but in the opposite direction. So, they will cover equal distance and the they will meet at the midpoint of A and B.

C is the midpoint of A and B.

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$C=\left(\dfrac{1+9}{2},\dfrac{1+11}{2}\right)$

$C=\left(\dfrac{10}{2},\dfrac{12}{2}\right)$

$C=\left(5,6\right)$

Therefore, the coordinates of point C are (5,6).