Prove that the points (1,-4),(3,14) and (2,5) are collinear?also find the intercepts made by the line on the axes.

Question

It is the question of opt math from class9

Answer 1

We can write y=mx+c where m=slope and c is the y intercept for amy pair of points. If the same equation fits all three points the points are collinear. m=(14-(-4))/(3-1)=(5-14)/(2-3)=(5-(-4))/(2-1)=9, This is sufficient to prove they are collinear.

So y=9x+c and 5=18+c, c=-13, y=9x-13. Plug in each point and you will find the equation is satisfied for each point.

Answer 2

Ar triangle formed by three points = ½{x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}

                                                      =½{1(14-5)+3(5+4)+2(-4-14)}

                                                       =½{ 9+27-36}

                                                        =0 
as the area of triangle formed by these three points is zero so the points must be co-linear