Point G is located at (3, −1), and point H is located at (−2, 3). Find the x value for the point that is 2 over 3 the distance from point G

Point G is located at (3, −1), and point H is located at (−2, 3). Find the x value for the point that is 2 over 3 the distance from point G to point H.

$$\\x=(1-\lambda)*3 + \lambda*(-2) \quad | \quad x_g=3 \quad and \quad x_h = -2 \\\\ \text{if } \lambda=\textcolor[rgb]{1,0,0}{0} \Rightarrow x = (1-\textcolor[rgb]{1,0,0}{0})*3+\textcolor[rgb]{1,0,0}{0}*(-2) = 3 = x_g \\ \text{if } \lambda=\textcolor[rgb]{1,0,0}{1} \Rightarrow x = (1-\textcolor[rgb]{1,0,0}{1})*3+\textcolor[rgb]{1,0,0}{1}*(-2) = -2 = x_h\\\\ \text{if } \lambda=\textcolor[rgb]{1,0,0}{{2\over3 }} \Rightarrow x = (1-\textcolor[rgb]{1,0,0}{{2\over3}} )*3+\textcolor[rgb]{1,0,0}{{2\over3}} *(-2)\\ \Rightarrow x={1\over3}*3 - {4\over3}\\ \Rightarrow x=-{1\over 3}$$

Notice that the distance between x values is just 3- (-2) = 5

And (2/3) of this is just 10/3

And we want 2/3 of the distance from G to H.

So,  3 - 10/3 = 9/3 - 10/3 = -1/3  and that's the value of the x coordinate that is 2/3 of the distance from G to H.