Question

In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC. What is the area of triangle DEC

Answer 1

5

Explanation:

The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:

E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )

= ( (0 + 2) / 2, (0 + 5) / 2 )

= (1, 2.5)

So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.