Question

points a(5 -1) b(-3 2) c(-1 8) are vertices of a triangle abc find the length of median from a. also find the coordinates of the centroid of this triangle

Answer 1

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Answer 2

Length of the median is 9.22 units and the centroid is [$\frac{1}{3}, 3$] .

Step-by-step explanation:

Let the midpoint of B(-3,2) and C(-1,8) is D, then the coordinates of D are [$\frac{-1 - 3}{2}, \frac{8 + 2}{2}$] ≡ [-2,5].

Now, the length of the median connecting A(5,-1) and D(-2,5) will be

$\sqrt{(5 - (- 2))^{2} + (-1 - 5)^{2}} = 9.22$ units.

Now, the centroid divides the median in a 2 : 1 ratio.

Now, the coordinates of the centroid which divides the line segment AD in the ratio 2 : 1 internally will be given by

$[\frac{2(-2) + 5}{1 + 2}, \frac{2(5) + (- 1)}{1 + 2}]$ ≡ [$\frac{1}{3}, 3$] (Answer)