Question

F is the midpoint of line segment EG and H is the midpoint of line segment FI if E(-9,-4), G(-1,6) and H(4,-3). Find the coordinates of I

Answer 1

well, we know the points E and G, let's find the coordinates for F

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ E(\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad G(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 -9}{2}~~~ ,~~~ \cfrac{ 6 -4}{2} \right) \implies \left(\cfrac{ -10 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies \stackrel{ \textit{\LARGE F} }{(-5~~,~~1)}`

we know that H is the midpoint of FI, now, we know H and we also know F, let's say the coordindates for "I" are (x , y), so

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ F(\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad I(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -5}{2}~~~ ,~~~ \cfrac{ y +1}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE H} }{(4~~,~~-3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -5 }{2}=4\implies x-5=8\implies \boxed{x=13} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +1 }{2}=-3 \implies y+1=-6\implies \boxed{y=-7}`

Check the picture below.