In the given diagram, Triangle ABC...

Question

In the given diagram, ∆ABC is a right triangle with . Segment AB is divided into four equal parts.

The coordinates of point F are (__,__), and the coordinates of point G are (__,__).

Answer 1

Triangles ABC and DBG are similar by the AA criteria: the right angle, and the angle B. Similar shapes have proportional corresponding sides. Therefore, |BG| : |BC| = |BD| : |BA| = 3 : 4. We can get |BC| by taking the difference of the x-coordinates of points B and C. That length is going to be 9. Thus, from |BG| : 9 = 3 : 4, we get |BG| = 6.75. This means the coordinates of point G must be (-0.75, -3).

To get from point B to point F, we need to move left by 1/4 of the distance we'd move to get from B to A, and then move up by 1/4 of the distance we'd move to get from B to A. The distance we move left from B to A is 9 (same as |BC|), and the distance we move up from B to A is 2. Divide those by 4, and we get 2.25 and 0.5. By moving left by 2.25 and up by 0.5 from point B, we get to F. Therefore point F must have the coordinates of (3.75, -2.5) .