Question

\( \triangle A B C \) lies in the plane with \( A (0,0), B (0,1) \) and \( C (1,0) \). Points M and N are chosen on \( A B \) and \( A C \), respectively, such that MN is parallel to BC and MN divides the area of \( \triangle A B C \) in two equal parts. Find the coordinates of \( M \). Ans. \( (0,1 / \sqrt{2}) \)

Answer 1

The area of triangle ABC is equal to 1/2.

Therefore the area of the two equal parts must be 1/4.

And the values of M and N are equal since they are parallel to B and C.

So we have the area of triangle AMN to be 1/2(y²) = 1/4

Or y = 1/√ 2

This makes the coordinates of point M to be (0, 1/√ 2)