Answer:
A.[tex]\frac{RP}{SP}=3[/tex]
B.[tex]\frac{RP}{RS}=\frac{3}{4}[/tex]
Step-by-step explanation:
We are given that three collinear points on the coordinate plane are
[tex]R(x,y),S(x+8h,y+8k) and P(x+6h,y+6k)[/tex]
A.We have to find the value of [tex]\frac{RP}{SP}[/tex]
Distance formula :[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using this formula and substitute the values then we get
RP=[tex]\sqrt{(x+6h-x)^2+(y+6k-y)^2}[/tex]
RP=[tex]\sqrt{36h^2+36 k^2}[/tex]
RP=[tex]6\sqrt{h^2+k^2}[/tex]
SP=[tex]\sqrt{(x+6h-x-8h)^2+(y+6k-y-8k)^2}[/tex]
SP=[tex]\sqrt{4h^2+4k^2}[/tex]
SP=[tex]\sqrt{4(h^2+k^2)}[/tex]
SP=[tex]2\sqrt{h^2+k^2}[/tex]
[tex]\frac{RP}{SP}=\frac{6\sqrt{h^2+k^2}}{2\sqrt{h^2+k^2}}[/tex]
[tex]\frac{RP}{SP}=3[/tex]
B.We have to determine the value of [tex]\frac{RP}{RS}[/tex]
RS=[tex]\sqrt{(x+8h-x)^2+(y+8k-y)^2}[/tex]
RS=[tex]\sqrt{64h^2+64k^2}[/tex]
RS=[tex]\sqrt{64(h^2+k^2)}[/tex]
RS=[tex]8\sqrt{h^2+k^2}[/tex]
[tex]\frac{RP}{RS}=\frac{6\sqrt{h^2+k^2}}{8\sqrt{h^2+k^2}}[/tex]
[tex]\frac{RP}{RS}=\frac{3}{4}[/tex]
