# Just how to get a formula that result completion factor of an angle line in rectangular shape?

When attracting an angle line (45 levels) in a rectangular shape from a basic factor $p = (x,y)$ that situated on the right or the leading line of the rectangular shape. Just how can I locate the junction factor $p2$ of this line with the rectangular shape?

To put it simply, I intend to write the target factor, $p2$, with my existing details: $x, y, w, h$. (This variables are defined aware listed below).

The factor $(0,0)$ remains in the top-right edge.

Alright, I'm not 100% certain I'm recognizing this appropriately. You claim that p can be situated on the right or leading line which p2 can be situated under or left line. Do you suggest the rectangular shape can be revolved? If that's the instance, the inquiry needs to claim that p can be on the right or profits of the rectangular shape. Additionally, are you seeking 2 different solutions or one that functions both when p2 gets on all-time low and also on the left?

If you do suggest that the rectangular shape can be revolved, and also desire 2 various solutions, it's rather straightforward. First I'll manage when p2 gets on all-time low and also p gets on the right.

Given that p2 gets on the lower line we understand the y - coordinate is h, according to the layout. We additionally recognize that p is (0, y). As a result of the 45 level angle, we understand that the range in between p's y - coordinate and also the lower appropriate edge coincides as the range in between the lower appropriate edge and also p2's x - coordinate, which in this instance is p2's x - coordinate. Consequently, the works with of p2 are (h - y, h).

If p2 gets on the left and also p gets on all-time low, it's really comparable. Given that p2 gets on the left, it's x - coordinate is h. Because p gets on the x - axis, it's (x,0). As a result of the 45 level angle, the range in between the lower left edge and also p coincides as the range in between the lower left edge and also p2, which this moment offers us p2's y - coordinate. Consequently the works with of p2 are (h, h - x).

With any luck I recognized your purposes appropriately. Otherwise, I wish you can utilize my misconceptions to more boost your inquiry.

If it is simply $45$ levels, after that the solution is not really hard. Facility a coordinate system near the bottom left hand edge of the rectangular shape. Therefore the works with of the (??? ) factor are $(q,0)$ for some $q<w$.

Keep in mind that the due to the fact that theta is $45$ levels, $y=w-q$ (Isosceles appropriate triangular ). Therefore $q=w-y$, and also our factor is merely $(w-y, 0)\dots$