Question

(-5,6)(4,5)3:4 find the point that partitions the segment with the two given endpoints with the given ratio

Answer 1

The equation to find the point x with the ratio is:

`x=x_1+(a)/(a+b)(x_2-x_1)`

Now we replace the values of x1 and x2 and a=3 and b=4 so:

`x=-5+(3)/(3+4)(5-(-5))`

and we simplify so:

`\begin{gathered} x=-5+(3)/(7)(10) \\ x=-0.7 \end{gathered}`

And for y will be:

`y=y_1+(a)/(a+b)(y_2-y_1)`

we replace the values so:

`y=6+(3)/(3+4)(5-6)`

and we simplify it:

`\begin{gathered} y=6+(3)/(7)(-1) \\ y=5.6 \end{gathered}`

So the partition point will be: (-0.7 , 5.6)