Question

If the points (x,y),(-5,-2) and (3,-5) are collinear, then prove that 3x+8y+31=0.

Answer 1

For the points(x,y),(-5,-2)and (3,-5) are collinear the area of the triangle formed by the given points should be equal to zero

x(-2-(-5))+(-5)(-5-y)+3(y-(-2))=0
x(-2+5)-5(-5-y)+3(y+2)=0
3x+25+5y+3y+6=0
3x+8y+31=0

Answer 2

since it is given that the points are collinear so...1/2{x(-2+5)-5(-5-y)+3(y+2)}=0=>(-2x+5x+25+5y+3y+6)=0=>3x+8y+31=0..hence proved