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:

$x=x_1+\frac{a}{a+b}(x_2-x_1)$

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

$x=-5+\frac{3}{3+4}(5-(-5))$

and we simplify so:

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

And for y will be:

$y=y_1+\frac{a}{a+b}(y_2-y_1)$

we replace the values so:

$y=6+\frac{3}{3+4}(5-6)$

and we simplify it:

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

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