Question

The vertices of a `triangleOBC` are `O(0,0) , B(-3,-1), C(-1,-3)`. Find the equation of the line parallel to BC and intersecting the sides OB and OC and whose perpendicular distance from the origin is `1/2`.

Answer 1

Equation of line BC
`y+1=(-3+1)/(-1+3)(x+3)`
`y+1=-x-3`
`y=-x-4`
`y=-x+c-(1)`
`y+x-c=0`
`|(-C)/sqrt2|=1/2`
`C/sqrt2=1/2`
`C=1/sqrt2`
`y=-x+1/sqrt2`
`sqrt2y=-sqrt2x+1`
`sqrt2x+sqrt2y=1`.