Let's do this question, the image of point three, comma five by the line of symmetry, which is equal
to one by two is the point.
C, find the coordinates of C.
All right.
Pause the video, give it a try and then let's do it together.
All right.
We're back.
Let's do it together over here.
Why is equal to one by two X and it's nine, which we have not yet discussed.
So this is part of the general case.
Let me draw my axis over here and let me plot three comma five over here.
Now, this is the nine Y is equal to one by two X..
Now, I need to find the reflection of this point about this line.
That means I need to draw a line which is perpendicular to Y is equal to one by two X and it passes
through three comma five.
And after this, I need to find a point on this line which is equidistant from this line right as the
distance of this point from this line.
Now this line over here will be Y is equal to minus two explicit.
Can you tell me why?
Because over here the slope is one by two.
Right.
Therefore, the slope over here has to be minus two because these two have to be perpendicular and one
by two in the minus two gives me minus one.
Right now, this line passes through this point over here.
Right.
So let me substitute this point into this line that gives me five into five is equal to minus two in
the three, plus C or C is equal to eleven.
All right.
Now, that means this line over here is why is equal to minus two X plus 11.
All right.
Now, let me substitute Y is equal to one by two X into this equation, because these two lines are
intersecting at this point.
And I'm trying to find out this point.
OK, so one by two X is equal to minus two X plus 11 or five by two.
X is equal to 11.
And that gives me X is equal to 22 by five.
Now we know why is equal to one by two X.
So if X is equal to twenty two by five, Y will be eleven by five.
Right.
All right.
So that is this point over here.
That's twenty two by five comma.
Eleven by five.
Now let this point C be equal maybe.
Now, this point is the reflection of a about this line, right, that means the distance, Abe.
Has to be equal to the distance C or it means that B is the midpoint of nine segment AC.
Right.
OK, let me make some space over here, if by the midpoint of AC, that means a plus three by two should
give me 22 by five, right.
OK, so that means is equal to forty four by five, minus three, which is equal to twenty nine by five,
similarly B plus five by two should be equal to eleven by five.
That is basically twenty two by five minus five, or that's equal to minus three by five.
And hence the answer that is the coordinates of point C is twenty nine by five comma minus three by
five.