Question

y у B (10, 10) А. (2, 4) Find point C so that that the ratio of length AC to the length of CB is 1:3.

Answer 1

The coordinates of the point C which divides the segments joining the points A(x1, y1) and B(x2, y2) in the ratio a:b are calculated as follows:

`C(x_1+(a)/(a+b)(x_2-x_1),y_1+(a)/(a+b)(y_2-y_1))`

Substituting with A(2, 4), B(10, 10) and the partition ratio 1:3, we get:

`\begin{gathered} C(2+(1)/(1+3)(10-2),4+(1)/(1+3)(10-4)) \\ C(2+(1)/(4)\cdot8,4+(1)/(4)\cdot6) \\ C(4,(11)/(2)) \end{gathered}`