# Find values of k so that point (0,k) lies on the triangle formed by the lines y+3x+2=0, 3y-2x-5=0, 4y+x-14=0.

### 1 Answer | Add Yours

You need to remember that the coordinates of the point that lies on one of the sides of triangle need to verify the equation of the side such that:

`(0,k)` belongs to `y+3x+2=0` if `k + 3*0 + 2 = 0.`

You need to solve for k the equation `k + 3*0 + 2 = 0` such that:

`k + 3*0 + 2 = 0 =gt k + 2 =0 `

`k = -2`

`(0,k)` belongs to `3y - 2x - 5 = 0` if `3k - 2*0 - 5 = 0.`

`3k - 2*0 - 5 = 0 =gt3k - 5 = 0 =gt 3k = 5 =gt k = 5/3`

`(0,k)` belongs to `4y + x - 14 = 0` if `4k +0 - 14 = 0.`

`4k - 14 = 0 =gt k = 14/4 =gt k = 7/2`

**Hence, evaluating the values of k if it lies on one of the sides of triangles yields `k = -2 ; k = 5/3 ; k = 7/2` .**