Find the coordinates of a point that divides the directed line segment PQ in the ratio 5:3.
A) (4,5)
B) (-6, 6)
C) (2, 2)
D) (4,1)

C

Step-by-step explanation:

Let the coordinates be (m, n) then by using the section formula we have

m=(5*8+3*(-8))/(5+3)=2

n=(5*(-1)+3*(7))/(5+3)=2

The point is (2,2)

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb