Answers:
Well, you already know off the bat that median AD is going to "bisect" side BC of the triangle.
What is the slope of side BC?
B(5,-3) = (x_1, y_1)
C(-7,7) = (x_2, y_2)
slope m=(y2 - y1) / (x2 - x1) = (7 - -3) / (-7 - 5) = 10/(-12)
okay... so halfway would mean 5 / -6
so... a change in y of 5 and a change in x of -6
so... point D is D(5 - 6, -3 + 5) = D(-1, 2)
Now you just have to use the distance formula to find the length of median AD... so you need to find the distance between point A(-2,6) and D(-1, 2)
Distance formula is ...
d = sqrt [(x2-x1)^2 + (y2-y1)^2]
.= sqrt [(-2 - -1)^2 + (6 - 2)^2]
.= sqrt [(-2 +1)^2 + 4^2]
.= sqrt [(-1)^2 + 16]
.= sqrt (1 + 16)
.= sqrt 17
Hence, the length of median AD of triangle ABC is (sqrt 17)
The solution is quite easy. Find the midpoint of B & C, to get the point D (-1,2). So AD =root[{(-2)-(-1)}^2+(6-2)^2] = root17
D is midpoint of BC. Therefore its co-ordinates are (-1,2). Now AD = SQRT(16+1)
= SQRT(17) ... ANSWER
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