In the diagram below of triangle E, F, GEFG, HH is the midpoint of start overline, E, G, end overline
EG
and II is the midpoint of start overline, F, G, end overline
FG
. If H, I, equals, minus, 3, x, plus, 14HI=−3x+14, and E, F, equals, 15, plus, 7, xEF=15+7x, what is the measure of start overline, E, F, end overline
EF
?
Since HH is the midpoint of start overline EG, end overline EG, HE is equal to GH. Similarly, II is the midpoint of start overline FG, end overline FG, FI is equal to IG.
Therefore, we can set up the following equations:
HE = GH
15 + 7x = -3x + 14
10x = -1
x = -0.1
Now that we have found the value of x, we can substitute it back into EF = 15 + 7x to find the measure of start overline EF, end overline EF:
EF = 15 + 7(-0.1)
EF = 15 - 0.7
EF = 14.3
Therefore, the measure of start overline EF, end overline EF is 14.3.