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.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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` .

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