Answer:
A: y-axis, x-axis, y-axis, x-axis
Explanation:
Given : A triangle ABC on the coordinate plane with point A at (1, 2) point B at (2, 4) and point C at (3, 0)
To Find: What set of reflections would carry triangle ABC onto itself?
Solution:
Option A: y-axis, x-axis, y-axis, x-axis
First Step : Reflect it about axis
So, its image will be in second quadrant
Second Step : Reflect the obtained image about x axis
So, its image will be in third quadrant.
Third step : Reflect the obtained image about y axis
So, its image will be in fourth quadrant .
Fourth step : Reflect the obtained image about x axis
So, its image will be in first quadrant .
So, By Option A set of reflections would carry triangle ABC onto itself
Option B : x-axis, y=x, y-axis, x-axis
y=x will give an inverse function image.
So, option B is wrong.
So, Option B set of reflections would not carry triangle ABC onto itself
Option C:x-axis, y-axis, x-axis
First Step : Reflect the triangle about x axis
So, its image will be in fourth quadrant.
Second step : Reflect the obtained image about y axis
So, its image will be in third quadrant .
Third step : Reflect the obtained image about x axis
So, its image will be in second quadrant .
So, Option C set of reflections would not carry triangle ABC onto itself.
Option D : y=x, x-axis, x-axis,y=x will give an inverse function image.
So, option D is wrong.
So, Option D set of reflections would not carry triangle ABC onto itself
Hence Option A is correct.
A: y-axis, x-axis, y-axis, x-axis