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

The volume of the rectangular prisms is

The sides of the top rectangular prism is  

The sides of the Bottom rectangular prism is

Add the volume of the two rectangular prisms to get