Students in this video, let's discuss the general case where we reflect a point about a line.
So let me have my X and Y axis over here.
Now, let me draw any line over here.
OK, now let it not be one of the special cases, right?
Because in these cases, we directly know how to write the answer.
Now, over here I have a point, OK?
And I need to reflect this point about this line over here.
So what do we do?
We have to draw a line that is perpendicular to this line and that passes through this point.
That would be this line over here.
Then we need to identify a point on the other side of the line, which is of the same distance as this
point from this line.
So this if this distance is D, then we need to find this point over here, which is also at a distance
of B from this line over here.
And then this would be the reflection of point A about line.
Now, if the equation of L is given, how do you proceed?
You start with identifying the equation of the perpendicular line.
Right.
That passes through it.
And then you find B using the fact that these two distances have to be equal.
Right.
You can easily find at this point that is the point of intersection of this line and this line, because
you can find the equation of this line, right.
Because you know that it's perpendicular to L and it passes through it.
Now, once you know this equation, you can find the point of intersection and then you can see that
this point and this point will have this point as its midpoint.
And using the fact that this is the midpoint, you can easily find the coordinates of Point B.
Now, we will do one of these questions in the example radius to make it more clear.