calculate the new end points of line after rotating an angle
i have two lines, one is slanted line and another is a straight line. Both the lines share same X coordinate separated by distance d. The straight line is rotated to an angle θ (which also needed to be calculated from slanted line) ,making it parallel to the slanted line. Now how to calculate the new end points X2,Y2 of the rotated line?
- I used the slope equation to find the m1 of the slanted line and then converted it into angle using m=tanθ formula.
- Now how to calculate the new X2,Y2 after rotating the line?
2 Answers
$\begingroup$No need to compute any angles or trigonometric functions of them directly. Since you want to end up parallel to the second line segment after rotation, you already have a vector that’s pointing in the right direction, namely $P_4-P_3$. You just need to adjust its length and add it to $P_0$: $$P_2=P_0+{\lvert P_1-P_0\rvert\over\lvert P_4-P_3\rvert}(P_4-P_3).$$
$\endgroup$ 4 $\begingroup$Let $AB$ the segment from $(x_0,y_0)$ to $(x_1,y_1)$. Note that when you rotate the segment $AB$ this point that we call $P$ rotates, describing an arc of angle $\theta$.
So, let the origin $O(x_0,y_0)$, and draw the perpendicular line to the segment $AB$ from $S(x_2,y_2)$. Let $K$ the intersection, the triangle $SOK$ is a right triangle. So:$$x_2=|x_1|\cos(\theta)$$and:$$y_2=|x_1|\sin(\theta)$$Note that we can write $|x_1|$ bevause we assume that the segment $AB$ is part of $x-$axis.
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