is this the answer: (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1) Substituting the given points: (y - 5)/(x - 1) = (0 - 5)/(0 - 1) (y - 5)/(x - 1) = -5/-1 (y - 5)/(x - 1) = 5 y - 5 = 5(x - 1) y - 5 = 5x - 5 y = 5x Diagonal BD: Using points B(6,9) and D(5,-3), similarly: (y - 9)/(x - 6) = (-3 - 9)/(5 - 6) (y - 9)/(x - 6) = -12/-1 (y - 9)/(x - 6) = 12 y - 9 = 12(x - 6) y - 9 = 12x - 72 y = 12x - 63 Now, to find the point of intersection, we solve these two equations simultaneously: y = 5x y = 12x - 63 Setting them equal: 5x = 12x - 63 7x = 63 x = 9 Substitute x = 9 into either equation to find y: y = 5(9) y = 45 So, the point of intersection of the diagonals is (9, 45)