Question

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?

Answer 1

Which of the following coordinates is the solution to this system? The coordinate grid below represents a system of linear equations.A.(0, 3)B.(0, -3)C.(3, -2)D.(-3, 2

Explanation:

The answer is A Because the plane is 3/0 wide and the length is way longer then that so its 3,0

Answer 2

The ratio RS:ST is 2:3.

We will use the distance formula:

`d=√((y_2-y_1)^2+(x_2-x_1)^2)`

The distance from R to S is:

`d=√((-5--3)^2+(-6--2)^2) \\ \\=√((-5+3)^2+(-6+2)^2) \\ \\=√((-2)^2+(-4)^2) \\ \\=√(4+16)=√(20)=√(4*5)=2√(5)`

The distance from S to T is:

`d=√((-3-0)^2+(-2-4)^2) \\ \\=√((-3)^2+(-6)^2)=√(9+36)=√(45) \\ \\=√(9*5)=3√(5)`

The ratio of RS to ST is then

`(2√(5))/(3√(5))`

Since √5 cancels out on the top and bottom, we are left with
2/3 = 2:3