subhakam wrote:Hello Anurag - I did not understand the question or the solution - What does the term "reflection mean" ?
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I totally misunderstood the question. Appreciate if you could explain it to me
In coordinate geometry, reflection over or with respect to a line means as if there is a invisible mirror placed on the line. For example, in the following figure P' is the reflection of P with respect to the line l, meaning as if there is an invisible mirror along the line l on which P' is the reflection of P.
Now according to the law of reflection,
- 1. Shortest distance of P from l = Shortest distance of P' from l
2. The straight line joining P and P' will be perpendicular to the line l
Now in our case a straight line (y = px + q) is reflected with respect to another straight line, y = x. This means we have to consider that an invisible mirror is placed along y = x and y = px + q is reflected on it. Refer to the following figures,
In the first figure, the black line is y = x and assume that the blue line is y = px + q. In the second figure, the red line is the reflection of the blue line over the black line.
The concept can be similarly extended to more complex shapes like triangle, circles etc also.
I hope this helps you to get an idea of what reflection means.
There are formulas to find out what will be the equation of a reflected line over an axis or another line etc. However, we can solve this particular question without any such formula. We just need to understand that we need to know whether slopes of the reflection of y = px + q is equal to m or not. This in turn means we need to know the slope of y = px + q, i.e. p and m.
Now, you can follow my reply or aneesh.kg's reply for a more detailed mathematical approach.
