Question

9. Find the equation of the median from the vertex R in a 3PQR with vertices at
P(1, -3), Q(-2, 5) and R(-3, 4).

Answer 1

Let S is the midpoint of line joining points P and Q, then RS is median.
so, first of all we have to find co-ordinate of S
use midpoint section formula,
e.g., S(x,y) is the midpoint of line joining the points P(1,-3) and Q(-2,5) ,
Then, x = (1 - 2)/2 = -1/2 and y = (-3 + 5)/2 = 1
so, S ≡ (-1/2, 1)

Now,slope of RS = (4 - 1)/(-3 + 1/2) = 3/(-5/2) = -6/5
equation of line RS (y -4) = -6/5(x + 3)
⇒5(y - 4) + 6(x + 3) = 0
⇒ 5y - 20 +6x + 18 = 0
⇒6x + 5y -2 = 0

Hence, equation of median from vertex R in PQR is 6x + 5y -2 = 0

Answer 2

ii ) Equation of Median P(-3,4) = ( x1,y1)

and M(-1/2,1) = ( x2 , y2 ) is

y - y1 = [ (y2-y1)/(x2-x1)](x-x1)

=> y-4 =[(1-4)/(-1/2+3)](x+3)

=> y-4 =[ (-3)/(5/2)](x+3)

=> y-4 = (-6/5)(x+3)

=>5(y-4) = (-6)(x+3)

=> 5y - 20 + 6(x + 3 ) = 0

=> 5y - 20 + 6x + 18 = 0

=> 6x + 5y - 2 = 0

Therefore ,

Required equation of the median ,

6x + 5y - 2 = 0

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