Question

Find a point K on the segment with endpoints F(-8, 10) and G(8, -2) that

Answer 1

Given:

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

Point K partitions the segment, starting at point F $\dfrac{3}{4}$ 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

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

According to the given information,

$\dfrac{FK}{FG}=\dfrac{3}{4}$

$FK:FG=3:4$

Now,

$FK:KG=FK:(FG-FK)$

$FK:KG=3:(4-3)$

$FK:KG=3:1$

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

Using the section formula, we get

$K=\left(\dfrac{3(8)+1(-8)}{3+1},\dfrac{3(-2)+1(10)}{3+1}\right)$

$K=\left(\dfrac{24-8}{4},\dfrac{-6+10}{4}\right)$

$K=\left(\dfrac{16}{4},\dfrac{4}{4}\right)$

$K=\left(4,1\right)$

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