How are the coordinates of a new point found if the point is reflected through the line y = x? How are the coordinates of the new point found if the point is reflected through the origin?

Question

anonymous · Answer

@cambrige help?

mathmate · Answer

New point on image of reflection about y=x can be found by exchanging x and y.
For example, the point (a,b) reflected about y=x is (b,a).

mathmate · Answer

Through the origin would be changing the signs of both x and y.
For example, (p,q) reflected through the origin would become (-p, -q)
this is the equivalent of rotating through 180 degrees.

anonymous · Answer

how are the coordinates of the new point found if it is translated right/left and up/down?
@mathmate

mathmate · Answer

Right-left:
if g(x) is the image (translated function) and f(x) is the original function
then g(x)=f(x-h) to translate f(x) h units to the $ right$.

Up-down
if g(x) is the image, and f(x) is the original function, then
g(x)=f(x)+k
where k is the translation upwards.

Change the sign of h and k to negative if the translation direction is to the left or down.

anonymous · Answer

thank you!!!

mathmate · Answer

yw!

anonymous · Answer

just rem this y=cx is always a line passing thru origin,c=slope

mathmate · Answer

y=cx is always a line through the origin.
However, the reflection about y=cx is more complex.  It requires the calculation of the values of sin/cos of the slope.  Usually it is done using matrix multiplication.