Question

Show that three successive reflections about x-axis, y-axis, and x-axis in sequence is equivalent to single reflection about y-axis

Answer 1

Following are the proff of the three successive reflections about the x-axis, y-axis and there reflection is given below

Explanation:

Let the function $Y=f(X)$

• Evaluating the reflection on the Y-axis, we obtain the image i.e (-x, y) for every point (x, y) on the slope.

So the  $Y = f(X)$   reflection mirror image reflection inside Y axis that will be written as $Y = f(-X).$

• Let imagine the three thoughts in the succession.

For every point ( X , Y) on the slope we get the point (X,-Y), the reflection around the x-axis will be.          

So  Y = f(X) is Y=-f(X) on reflection

1st. Y=-f(-X) gives the second reflection across the Y axis.

Also the third X-axis reflection gives us $Y=-(-f(-X)\ which\ is\ Y = f(-X).$

Sothe third X-axis reflection gives us $Y=-(-f(-X) \ which\ is\ Y = f(-X).$

Learn More :

• brainly.com/question/10705184