Answer:
Coordinates of point C that is two-third the distance from point G to point H is (-0.33,1.67)
Step-by-step explanation:
Given that Point G is located at (3, -1) and point H is located at (-2, 3). we have to find out the point that is two-third the distance from point G to point H which means in ratio 2:1
When any point divides a segment in ratio m:n, we use the section formula to find the coordinates of that point.
The coordinates of the point C that divides the line segment joining the points G(3,-1) and point H(-2,3) in ration m:n i.e 2:1 is
[tex]C=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex]
[tex]=(\frac{2(-2)+1(3)}{2+1}, \frac{2(3)+1(-1)}{2+1})[/tex]
[tex]=(\frac{-1}{3},\frac{5}{3})[/tex]
[tex]=(-0.33,1.67)[/tex]
Hence, coordinates of point C that is two-third the distance from point G to point H is (-0.33,1.67)
