Answer:
see explanation
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
(g)
with (x₁, y₁ ) = P (p, 4p) and (x₂, y₂ ) = Q (- 2p,8p)
d = [tex]\sqrt{(-2p-p)^2+(8p-4p)^2}[/tex]
= [tex]\sqrt{(-3p)^2+(4p)^2}[/tex]
= [tex]\sqrt{9p^2+16p^2}[/tex]
= [tex]\sqrt{25p^2}[/tex]
= 5p
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(h)
with (x₁, y₁ ) = R (- 2m, 5m) and (x₂, y₂ ) = S (- 4m, - 2m)
d = [tex]\sqrt{(-4m-(-2m))^2+(-2m-5m)^2}[/tex]
= [tex]\sqrt{(-4m+2m)^2+(-7m)^2}[/tex]
= [tex]\sqrt{(-2m)^2+49m^2}[/tex]
= [tex]\sqrt{4m^2+49m^2}[/tex]
= [tex]\sqrt{53m^2}[/tex]
= m[tex]\sqrt{53}[/tex]
