Question

if x - 3y + k = 0 is a median of the triangle whose vertesis are at points a (-1,3) b (0,4) c (-5,2) then the value of k is

Answer 1

Step-by-step explanation:

Given :-

x - 3y + k = 0 is a median of the triangle whose vertesis are at points A (-1,3) , B (0,4) and C (-5,2)

To find :-

Find the value of k ?

Solution :-

Given points are A (-1,3) , B (0,4) and C (-5,2)

Let (x1, y1) = (-1,3) => x1 = -1 and y1 = 3

Let (x2, y2) = (0,4) => x2 = 0 and y2 = 4

Let (x3, y3) = (-5,2) => x3 = -5 and y3 = 2

We know that

The coordinates of the centroid of a triangle formed by (x1, y1) , (x2, y2) and (x3, y3) is ( (x1+x2+x3)/3 , (y1+y2+y3)/3 )

The Centroid = ( (-1+0-5)/3 , (3+4+2)/3 )

=> The Centroid = ( -6/3 , 9/3 )

=> The Centroid = (-2,3)

According to the given problem

The median is x - 3y + k = 0

Now , put x = -2 and y = 3 in the equation then

=> -2-3(3)+k = 0

=> -2-9+k = 0

=> -11+k = 0

=> k = 0+11

=> k = 11

Therefore, k = 11

Answer:-

The value of k for the given problem is 11

Used formulae:-

→The coordinates of the centroid of a triangle formed by (x1, y1) , (x2, y2) and (x3, y3) is ( (x1+x2+x3)/3 , (y1+y2+y3)/3 )