Question

Three collinear points on the coordinate plane are r(x,y), s(x+8h, y+8k), and p (x+6h, y+6k)

Answer 1

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

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

Step-by-step explanation:

The complete question is

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

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

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

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

step 1

Find the distance RP

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

substitute the values in the formula

`RP=√((x+6h-x)^2+(y+6k-y)^2)`

`RP=√(36h^2+36 k^2)`

`RP=6√(h^2+k^2)`

step 2

Find the distance SP

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

substitute the values in the formula

`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)`

step 3

Find the ratio RP/SP

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

`(RP)/(SP)=3`

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

step 1

Find the distance RS

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

`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)`

step 2

Find the ratio RP/RS

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

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