Answer:
Condition for collinearity of three points on a line.
Explanation:
We are given the following information in the question:
Point X, Y and Z lies on a line m.
We have to show that these points are collinear. Three points on a point are collinear if the area of triangle formed by these three points is zero.
We make the following assumptions.
Let
be the coordinates of point X, Y and Z respectively.
Then the area of triangle formed by these three points is given by:
![(1)/(2)\left[\begin{array}{ccc}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{array}\right] }](https://img.qammunity.org/2017/formulas/mathematics/high-school/9cq5vm6ucflr926m6z14i69ievgkzb3tls.png)
Equating area of triangle to zero,
![\left[\begin{array}{ccc}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{array}\right] } = 0](https://img.qammunity.org/2017/formulas/mathematics/high-school/gbzilwh5r9hccjss7y1ga5pfvor75hr8dq.png)
Hence, the above condition is the condition foe collinearity of three points on a given line.