Respuesta :
Answer:
A.[tex]\frac{RP}{SP}=3[/tex]
B.[tex]\frac{RP}{RS}=\frac{3}{4}[/tex]
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
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]R(x,y),S(x+8h,y+8k) and P(x+6h,y+6k)[/tex]
Part A.We have to find the value of [tex]\frac{RP}{SP}[/tex]
step 1
Find the distance RP
[tex]R(x,y),P(x+6h,y+6k)[/tex]
substitute the values in the formula
[tex]RP=\sqrt{(x+6h-x)^2+(y+6k-y)^2}[/tex]
[tex]RP=\sqrt{36h^2+36 k^2}[/tex]
[tex]RP=6\sqrt{h^2+k^2}[/tex]
step 2
Find the distance SP
[tex]S(x+8h,y+8k),P(x+6h,y+6k)[/tex]
substitute the values in the formula
[tex]SP=\sqrt{(x+6h-x-8h)^2+(y+6k-y-8k)^2}[/tex]
[tex]SP=\sqrt{4h^2+4k^2}[/tex]
[tex]SP=\sqrt{4(h^2+k^2)}[/tex]
[tex]SP=2\sqrt{h^2+k^2}[/tex]
step 3
Find the ratio RP/SP
[tex]\frac{RP}{SP}=\frac{6\sqrt{h^2+k^2}}{2\sqrt{h^2+k^2}}[/tex]
[tex]\frac{RP}{SP}=3[/tex]
Part B. We have to determine the value of [tex]\frac{RP}{RS}[/tex]
step 1
Find the distance RS
[tex]R(x,y),S(x+8h,y+8k)[/tex]
[tex]RS=\sqrt{(x+8h-x)^2+(y+8k-y)^2}[/tex]
[tex]RS=\sqrt{64h^2+64k^2}[/tex]
[tex]RS=\sqrt{64(h^2+k^2)}[/tex]
[tex]RS=8\sqrt{h^2+k^2}[/tex]
step 2
Find the ratio RP/RS
[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]