Answer:
RS : ST = 2 : 3
Step-by-step explanation:
Coordinates of the endpoints of the line RT are R(-6, -5) and T(4, 0).
One point S has been given on line RT with the coordinates as(-2, -3)
Now we have to find the ratio between RS and ST.
Since distance between two points is measured by the formula
D = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
Where endpoints of the line are (x, y) and (x', y')
Now we plug in the values of points R and S in the formula to get the length of RS.
RS = [tex]\sqrt{(-6+2)^{2}+(-5+3)^{2}}[/tex]
= [tex]\sqrt{(-4)^{2}+(-2)^{2}}[/tex]
= [tex]\sqrt{(16+4}[/tex]
= [tex]\sqrt{20}[/tex]
= [tex]2\sqrt{5}[/tex] units
Now ST = [tex]\sqrt{(-2-4)^{2}+(0+3)^{2}}[/tex]
= [tex]\sqrt{(-6)^{2}+(3)^{2}}[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
= [tex]3\sqrt{5}[/tex]
Now the ratio of RS and ST will be
[tex]\frac{RS}{ST}=\frac{2\sqrt{5} }{3\sqrt{5} }[/tex]
Or RS : ST = 2 : 3
