Question

Given the points R (6,-2) and T (-9,- 7), find the coordinates of point S on line RT such that the ratio of RS to ST is 3 : 2​ plz help

Answer 1

Answer:

(-3, -5)

Step-by-step explanation:

By using the distance formula, we see that the length of RT is $\sqrt{(6+9)^2+(-2+7)^2}$ which equals $5\sqrt{10}$.

The ratio of RS to ST is 3:2, so we can write the distance of RS as $(5\sqrt{10} / 5) * 3$ which equals $3\sqrt{10}$. The distance of ST is then $2\sqrt{10}$.

Since we know the distance of RS and ST, we can find the coordinates of point S by using the distance formula again:

$\sqrt{(6-x)^2+(-2-y)^2} = 3\sqrt{10}$ and $\sqrt{(-9-x)^2+(-7-y)^2} = 2\sqrt{10}$

We solve for x and y, getting (-3, -5).