Triangle ABC has vertices (0,0) ,(11,60) and (91,0). If the line y=kx cute the triangle into two triangles of equal area then k= ? Find the value of k

Question

The question is from the chapter Straight Lines

Answer 1

Any median shall bisect the triangle. 

For example a line connecting the origin with the midpoint of the opposite side (51, 30) shall bisect the triangle.

 

Can you derive the equation of this line?

Answer 2

Draw ΔABC.  Draw the altitude from (11,60) to the x-axis

 

  The base of the triangle has length 91 and the altitude has length 60.

 

  Area of ΔABC = (1/2)(91)(60) = 2730

 

Draw the line y = kx.  It intersects ΔABC at (0,0) and (x, kx).

 

  We want to find k so that the triangle with vertices (0,0), (91,0) and (x,kx) has area (1/2)(2730) = 1365.

 

So, (1/2)(91)(k) = 1365

 

             91k = 2730

 

                k = 30