I am working on a Higher Post-AP Math question and I am having trouble solving it. The question asks to find the length of the orthogonal projection of a line segment on a given line. Here are the details:
A straight line $l$ and the points $A$ and $B$ lie in a plane.
The length of the line segment $AB$ is 20 units.
The distance from point $A$ to the line $l$ is 2 units, and the distance from point $B$ to the line $l$ is 14 units.
I have attempted to solve the question, but I am not sure if my approach is correct. According to my understanding, there are two possible cases, depending on whether points $A$ and $B$ lie on the same side of the line $l$ or not. In the first case, I drew a line $m$ parallel to $l$ passing through $A$, and then drew normal lines from $A$ and $B$ to $l$. I found the intersection point of $m$ and the normal from $B$ to $l$, which I denoted as $C$. Then, I used the Pythagorean theorem to find the length of $AC$, which is the length of the orthogonal projection of the line segment $AB$ on $l$.
However, I am not sure if my approach is correct, and I would appreciate any guidance or suggestions on how to solve this question. Also, if there are any alternate methods to solve the question, please share them as well.
Thank you in advance!