What set of reflections would carry triangle abc onto itself?

triangle abc on the coordinate plane with point a at 1, 2, point b at 2, 4, and point c at 3, 0.

a: y-axis, x-axis, y-axis, x-axis
b: x-axis, y=x, y-axis, x-axis
c: x-axis, y-axis, x-axis
d: y=x, x-axis, x-axis

A: y-axis, x-axis, y-axis, x-axis

Step-by-step 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

answer: -8.2562234e+13