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Students in this video, let's discuss the general case where we reflect a point about a line.

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So let me have my X and Y axis over here.

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Now, let me draw any line over here.

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OK, now let it not be one of the special cases, right?

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Because in these cases, we directly know how to write the answer.

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Now, over here I have a point, OK?

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And I need to reflect this point about this line over here.

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So what do we do?

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We have to draw a line that is perpendicular to this line and that passes through this point.

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That would be this line over here.

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Then we need to identify a point on the other side of the line, which is of the same distance as this

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point from this line.

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So this if this distance is D, then we need to find this point over here, which is also at a distance

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of B from this line over here.

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And then this would be the reflection of point A about line.

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Now, if the equation of L is given, how do you proceed?

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You start with identifying the equation of the perpendicular line.

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Right.

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That passes through it.

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And then you find B using the fact that these two distances have to be equal.

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Right.

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You can easily find at this point that is the point of intersection of this line and this line, because

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you can find the equation of this line, right.

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Because you know that it's perpendicular to L and it passes through it.

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Now, once you know this equation, you can find the point of intersection and then you can see that

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this point and this point will have this point as its midpoint.

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And using the fact that this is the midpoint, you can easily find the coordinates of Point B.

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Now, we will do one of these questions in the example radius to make it more clear.