Given:

The points (-1, 2) and (5, 4).

To find:

The projection of the point (1, 0) on the line joining the points (-1, 2) and (5, 4).

Explanation:

Let A (− 1, 2) be the given point whose projection is to be evaluated and C (− 1, 2) and D (5, 4) be the other two points.

Also, let M (h, k) be the foot of the perpendicular drawn from A (− 1, 2) to the line joining the points C (− 1, 2) and D (5, 4).

Diagram:

Clearly, the slope of CD and MD are equal.

⇒ h – 3k + 7 = 0…….(1)

The lines segments AM and CD are perpendicular.

⇒ 3h + k – 3 = 0 …….(2)

Solving (1) and (2) by cross multiplication, we get:

Hence, the projection of the point (1, 0) on the line joining the points (-1, 2) and (5, 4) is