Question

the endpoints of line segment DEF are D(1,4) and and F(16,14). Determine and state the coordinates of E, if DE:EF = 2:3.

Answer 1

The coordinates can be obtained using section formula

`\begin{gathered} \text{Let the coordinates of D be (x}_(1_,)y_1)andFbe(x_2,y_2) \\ \text{The point E divides the line in m:n ratio.} \\ U\sin g\text{ section formula, coordinates of E is} \\ (mx_2+nx_1)/(m+n),\text{ }(my_2+ny_1)/(m+n) \\ \end{gathered}`
`\begin{gathered} (x_1,y_1)=(1,4),(x_2,y_2)=(16,14),\text{ m:n=2:3} \\ \text{Substitute the values in section formula} \\ (2\ast16+3\ast1)/(2+3),\text{ }(2\ast14+3\ast4)/(2+3) \\ (32+3)/(5),\text{ }(28+12)/(5) \\ (35)/(5),\text{ }(40)/(5) \\ 7,\text{ 8} \end{gathered}`

The x coordinate of E is 7 and y coordinate is 8.