Find a point K on the segment with endpoints F(-8, 10) and G(8, -2) that partitions the segment, starting at point F 3/4 of the way to point G

Given:

The endpoints of a line segment are F(-8, 10) and G(8, -2).

Point K partitions the segment, starting at point F of the way to point G.

To find:

The coordinates of point K.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are

According to the given information,

Now,

It means point K divides the segment in 3:1.

Using the section formula, we get

Therefore, the coordinates of the point K are (4,1).

hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)