Question:i am desperately waiting here for the answer. will be very grateful if you work out the problem and say me the answer with steps. it is based on coordinate geometry. i am having all the hopes on EduQnA.com community. please post ur reply if u know to solve it.

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)

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