Question

99. If a triangle has vertices are (-5,3), (1, -1), and (0,4)
then lengths of its three medians will be​

Answer 1

Answer:

Let the vertices of triangle are A(1, -1), B(0, 4) and C(-5, 3). Let AP, BQ and CR are medians drawn from vertices A, B and C respectively. The co-ordinate of mid point P of side BC. Hence, co-ordinate of P = (-5/2, 7/2) And co-ordinate of mid point Q of side CA. Now co-ordinate of mid point R of side AB = ((1 + 0)/2, (-1 + 4)/2) = (1/2, 3/2) Hence, the co-ordinate of R = (1/2, 3/2) ∴ Length of median AP = Distance between the points A(1, -1) and point p (-5/2, 7/2) Length of median BQ = Distance between the points B(0, 4) and Q(2, 1) Length of median CR = Distance between the points C(-5, 3) and R(1/2, 3/2) Hence length of median are √130/2, √13 and √130/2 respectivelyRead more on Sarthaks.com - https://www.sarthaks.com/757086/find-the-length-of-median-of-triangle-whose-vertices-are-1-1-0-4-and-5-3-respectively