Question

A point G on a segment on a segment with endpoints F(4, 8) and H(10, 12) partitions the segment in a 3:4 ratio. Find G. You must show all work to receive credit.

This is for Geometry

Answer 1

Suppose, we are given

two points as

F as (x1, y1)

H as (x2, y2)

assume  it divides  in m/n

we can use formula

$G=(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

now, we are given points as

F=(x1, y1)=(4,8)

$x_1=4,y_1=8$

H=(x2, y2)=(10,12)

$x_2=10, y_2=12$

$\frac{m}{n} =\frac{3}{4}$

so,

$m=3,n=4$

now, we can find  

$x=(\frac{3*10+4*4}{3+4}, y=\frac{3*12+4*8}{3+4})$

$x=\frac{46}{7} , y=\frac{68}{7}$

so, point is

$G=(\frac{46}{7} , \frac{68}{7})$.................Answer