Question

Three collinear points on the coordinate plane are R(x, y), S(x+8h, y+8k), and P(x+6h, y+6k).

Part A: Determine the value of RP/SP
Part B: Determine the value of RP/RS

Answer 1

USE THE DISTANCE FORMULA FOR EACH SEGMENT

Answer 2

A.
`(RP)/(SP)=3`

B.
`(RP)/(RS)=(3)/(4)`

Explanation:

We are given that three collinear points on the coordinate plane are

`R(x,y),S(x+8h,y+8k) and P(x+6h,y+6k)`

A.We have to find the value of
`(RP)/(SP)`

Distance formula :
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Using this formula and substitute the values then we get

RP=
`√((x+6h-x)^2+(y+6k-y)^2)`

RP=
`√(36h^2+36 k^2)`

RP=
`6√(h^2+k^2)`

SP=
`√((x+6h-x-8h)^2+(y+6k-y-8k)^2)`

SP=
`√(4h^2+4k^2)`

SP=
`√(4(h^2+k^2))`

SP=
`2√(h^2+k^2)`

`(RP)/(SP)=(6√(h^2+k^2))/(2√(h^2+k^2))`

`(RP)/(SP)=3`

B.We have to determine the value of
`(RP)/(RS)`

RS=
`√((x+8h-x)^2+(y+8k-y)^2)`

RS=
`√(64h^2+64k^2)`

RS=
`√(64(h^2+k^2))`

RS=
`8√(h^2+k^2)`

`(RP)/(RS)=(6√(h^2+k^2))/(8√(h^2+k^2))`

`(RP)/(RS)=(3)/(4)`