Question

(10, 10) А (2, 4) Find point C so that that the ratio of length Ad to the length of CB is 3:1

Answer 1

`(8,8.5)`

Step-by-step explanation

When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:

`((mx_2+nx_1)/(m+n),(my_2+my_1)/(m+n))`

where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.

Therefore, we have that:

`\begin{gathered} m=3;n=1 \\ (x_1,y_1)=(2,4) \\ (x_2,y_2)=(10,10) \end{gathered}`

Therefore, the coordinates of point C are:

`\begin{gathered} ((3\cdot10+1\cdot2)/(3+1),(3\cdot10+1\cdot4)/(3+1)) \\ ((30+2)/(4),(30+4)/(4)) \\ ((32)/(4),(34)/(4)) \\ (8,8.5) \end{gathered}`

Those are the coordinates of C.