Answer
(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle.
(b) The orthocenter of a right triangle is the vertex with the right angle.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/cc9b080c-94ca-4eb3-b9ef-f9c52185e117/result_image/1556866624.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013333Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=54d8c56526193031f27b2fdef83dbff97e92bbf4a90079d2438adbecb56f289f)
Work Step by Step
(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle.
(b) An altitude is a perpendicular line from a vertex of a triangle to the opposite side.
The orthocenter is the point where the three altitudes of a triangle intersect.
In the sketch, the altitude of vertex A is the line $AC$, and the altitude of vertex B is the line $BC$. Note that these two altitudes intersect at the point C. Also, the altitude of vertex C obviously includes the point C.
Therefore, the orthocenter of any right triangle is the vertex with the right angle.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/cc9b080c-94ca-4eb3-b9ef-f9c52185e117/steps_image/small_1556866624.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013333Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=bdca70d3556243bace679f09a6427249aaa017cc7c4a88f880f649cddad44bb7)