Question

(-9,3)(1,8) 2:3 find the point that partitions the segment with the two given endpoints with the given ratio

Answer 1

the given end points are ,

A(-9,3)

B(1,8)

the ratio is , m : n = 2: 3

the formula of parting a line in m: n is given as follows,

so the points will be,

`x=(mx_2+nx_1)/(m+n)`
`x=(2*1+3*-9)/(2+3)`

`\begin{gathered} x=(2-27)/(5)=(-25)/(5) \\ x=-5 \end{gathered}`

and the y-coordinate of the point is

`y=(2*8+3*3)/(2+3)`
`\begin{gathered} y=(16+9)/(5)=(25)/(5) \\ y=5 \end{gathered}`

thus, the point is (-5,5)

it means point P(-5,5) is dividing the line AB in ratio 2: 3

thus, the answer is (-5,5)