Answer to Question #219998 in Analytic Geometry for Jessy

Question

A slender rod 40 in long is bent so as to form a right triangle. If the segments are 8 in and 32 in long, find the centroid.

Answer 1

The centroid of a triangle is the point of intersection of its medians.

The centroid of a triangle divides each median in the ratio 2:1.

If the vertical segment is 32 in up and horisontal segment is 8 in right from the vertex of the right angle, then the first median is $y=-2x+16$ and the second median is $y=-8x+32.$

Intersection

$$-2x+16=-8x+32$$

$$6x=16$$

$$x=\dfrac{8}{3}$$

$$y=-2(\dfrac{8}{3})+16=\dfrac{32}{3}$$

The centroid is (32/3) in up and (8/3) in right from the vertex of the right angle,