 Hello friends, let's discuss the following question. It says if three points x0, a b and 0k lie on a line Show that a upon h plus b upon k is equal to 1 now if we have three points say a b c then they lie on the same line or they are collinear if slope of a b is equal to slope of Vc So this is the key idea Let us now proceed on with the solution the given three points are a h0 b a b and C 0k Now if these three points Lie on the same line that means they are collinear and this implies slope of a b Is equal to slope of bc now slope of a b is given by b minus 0 That is y2 minus y1 upon x2 minus x1 that is a minus H and Slope of bc is given by k minus b upon 0 minus a And this again implies b upon a minus h is equal to k minus b upon minus a Now cross multiplying we get minus a b is equal to a minus h into k minus b and This again implies minus a b is equal to a k minus a b minus h k Plus h b Now minus a b gets cancelled with minus a b and this implies one is equal to a k Minus h k Plus h b and this implies Since we have cancelled minus a b with minus a b here. We have 0 and now this implies h k is equal to a k plus h b Now dividing both sides by h k we have h k upon h k is equal to a k upon h k plus h b upon h k and This implies a upon h plus b upon k is equal to 1 Hence we have proved that a upon h plus b upon k is equal to 1 So this completes the question. Hope you enjoyed the session goodbye and take care