Question

if A(5,-1), B(-3,-2), C(-1,8) are the vetices of a triangle , the length of a median through A is ?

Answer 1

The median through A will bisect the line BC. So first we find the point which bisects BC in two equal halves

Let that point be D(X,Y). By section formula,

X=(-3-1)÷2

= -2

Y=(-2+8)÷2

=3

Hence the point (-2,3) divides BC in two halves. Now the median through A must pass through this point therefore the slope of the required line is (3+1)/(-2-5) = 4/-7. The required line is 3-y = 4/-7(x+2), i.e.,7y = 4x+29 this is the final answer. Thank you.

Answer 2

Question: If A(5,-1), B(-3,-2), C(-1,8) are the vertices of a triangle ABC, find the length of the median through A abd the coordinates of the centroid.

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