Question

the coordinates of the endpoints of line RT are R (-6,-5) and T (4,0), and point 2 is on line RT. The coordinate of S are (-2,-3). Which of the following represents the ratio RS: ST

Answer 1

RS : ST = 2 : 3

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 =
`\sqrt{(x-x')^(2)+(y-y')^(2)}`

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 =
`\sqrt{(-6+2)^(2)+(-5+3)^(2)}`

=
`\sqrt{(-4)^(2)+(-2)^(2)}`

=
`√((16+4)`

=
`√(20)`

=
`2√(5)` units

Now ST =
`\sqrt{(-2-4)^(2)+(0+3)^(2)}`

=
`\sqrt{(-6)^(2)+(3)^(2)}`

=
`√(36+9)`

=
`√(45)`

=
`3√(5)`

Now the ratio of RS and ST will be

`(RS)/(ST)=(2√(5) )/(3√(5) )`

Or RS : ST = 2 : 3

Answer 2

The ratio of RS:ST will evaluated as follows:
RS=√[(-2-(-6))²+(-3-(-5)²)]
RS=√(4²+2²)
RS=√(16+4)
RS=√20
Next
ST=√[(4-(-2))²+(0-(-3))²]
ST=√[(6²+3²)
ST=√45
hence:
RS:ST
=√20/√45
=(2√5)/(3√5)
=2/3
thus the ratio is 2:3