Question

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

Answer 1

help please

Answer 2

\(\bf G(3,-1)\qquad H(-2,3)\\ \quad \\ \quad \\

\color{blue}{\cfrac{HP}{GP}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot HP=ratio1\cdot GP\quad \textit{dividing by P}\\ \quad \\
ratio2\cdot H=ratio1\cdot G\implies} 2(-2,3)=3(3,-1)\\ \quad \\\qquad \color{blue}{P=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\ \quad \\

\qquad thus\qquad \\ \quad \\
P=\left(\cfrac{(2\cdot -2)+(3\cdot 3)}{2+3}\quad ,\quad \cfrac{(2\cdot 3)+(3\cdot -1)}{2+3}\right)\)

Answer 3

If P = (-4 +9)/(2 + 3) or 5/5 or 1 for the x and
(6 - 3)/(2 + 3) or 3/5 for y P (1, 3/5) Does this point even fall on the line?

The equation for the line that goes thru points H (-2,3) and G (3, -1) has a slope of -4/5 with slope intercept equation of y=(-4/5)(x) + 7/5, I don't think that the point found in the solution (1, 3/5) is on this line. Please comment if I have erred. @jdoe0001

Answer 4

@radar the graph shows the point P in the wrong location, it should be ratio1=3 and ratio2=2
however in the equation I used the proper ratio values for the equivalence

anyhow... the equation of this line is \(\bf y=-\cfrac{4}{5}+\cfrac{7}{5}\)

if you plug in 1 for "x", that is, x=1, you'd get the proper "y" value
if you notice the line itself, the ratio is about a 2:3 ratio from G to H
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiItKDQvNSl4Kyg3LzUpIiwiY29sb3IiOiIjRTMwOTA5In0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTAuMzYwNjU3NzE1MiIsIjEuODIwMzgwMzY0OCIsIjAuMDgzNzI4NzkzNTk5OTk5OTYiLCIxLjQyNTkwNjA3MzYiXX1d

Answer 5

I see it now, don't know what got into me. Thanks.