The cordinates of the endpoints of RT are R(-6,-5) and T(4,0), and point S is on RT. The coordinates of S are (-2,-3). Which of the following represent the ratio RS:ST?
Accepted Solution
A:
The ratio RS:ST is 2:3.
We will use the distance formula: [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The distance from R to S is: [tex]d=\sqrt{(-5--3)^2+(-6--2)^2}
\\
\\=\sqrt{(-5+3)^2+(-6+2)^2}
\\
\\=\sqrt{(-2)^2+(-4)^2}
\\
\\=\sqrt{4+16}=\sqrt{20}=\sqrt{4*5}=2\sqrt{5}[/tex]
The distance from S to T is: [tex]d=\sqrt{(-3-0)^2+(-2-4)^2}
\\
\\=\sqrt{(-3)^2+(-6)^2}=\sqrt{9+36}=\sqrt{45}
\\
\\=\sqrt{9*5}=3\sqrt{5}[/tex]
The ratio of RS to ST is then [tex]\frac{2\sqrt{5}}{3\sqrt{5}}[/tex]
Since √5 cancels out on the top and bottom, we are left with 2/3 = 2:3