Question

if three points (X1, Y1) , (X2, Y2) , (X3, Y3) lie on same line then prove that
Y2-Y3/X2X3 + Y3-Y1/X3X1 + Y1-Y2/X1X2 = 0​

Answer 1

Step-by-step explanation:

If 3 points (X1, Y1), (X2, Y2), (X3, Y3) lie on the same line, then prove that [(Y2 - Y3)/ X2X3] + [(Y3 - Y1)/ X3X1] + [(Y1 - Y2)/ X1X2] = 0?”

If the points are colinear then the slope of that line — call it m — can be expressed in 3 different ways depending between which points you are calculating it, but it will always be the same m: always equal to the change in y coordinate, divided by change in x coordinate between whatever 2 points you choose. So:

[math] \displaystyle m= \frac{y_2-y_3}{x_2-x_3}=\frac{y_3-y_1}{x_3-x_1}=\frac{y_1-y_2}{x_1-x_2}[/math]

Replace the y differences in the original eq. by m times the change in x.