Point r divides ef in the ratio 1: 5. if the coordinates of e and f are (4,8) and (11,4), respectively, what are the coordinates of of r to two decimal places?
a). (4.66, 7.62)
b). (6, 6.86)
c). (5.17, 7.33)
d). (9.83, 4.67)

Good morning,

if a line of points (x₁, y₁) and (x₂, y₂) is divided by ratio p : q

The new coordinates become    ( (px₂ + qx₁)/(p +q), (py₂ + qy₁)/(p +q) )    

E(4, 8) and F(11, 4), x₁ = 4, y₁ = 8,  x₂ = 11, y₂ = 4,  ratio p:q = 1:5, p =1, q = 5

(px₂ + qx₁)/(p +q) = (1*11 + 5*4)/(1 +5) = (11 + 20)/6 = 31/6 ≈ 5.17   to 2 decimal places.

(py₂ + qy₁)/(p +q) = (1*4 + 5*8)/(1 +5) = (4 + 40)/6 = 44/6 ≈ 7.33   to 2 decimal places.

So the coordinate R that divides EF in the ratio 1:5 is ≈ (5.17, 7.33) to 2 decimal places.

Option C is the answer.

I hope this helps.

-Olemakpadu