Triangle A is reflected in the x axis to give triangle B, which is then reflected in the line y=x to give Triangle C. Draw Triangle C.

Answer:

The coordinates of triangle C on the grid are

(-5,4) , (-2,2) and (-2,4)

Step-by-step explanation:

We can identify the coordinates of the vertices of the triangles so as to get a diagram

For the first triangle, we have the following coordinates;

(4,5) , (2,2) and (4,2)

Now, let us get the coordinates of triangle B after reflecting triangle A in the x-axis

what we have in this case is that the x-axis coordinates stays same while the y-axis values are negated

Hence, the coordinates of triangle B are;

(4,-5) , (2,-2) and (4,-2)

Lastly we are to reflect triangle B in the line y = x so we get triangle C

A reflection over the line y= x means that we are going to switch the place of the x and y coordinates of the pre-image

So, the coordinates of triangle C are;

(-5,4) , (-2,2) and (-2,4)

The coordinates of triangle C are  (-5,4) , (-2,2) and (-2,4)

From the given image the vertices of the triangles are

Triangle A has coordinates (4,5) , (2,2) and (4,2)

After reflecting triangle A in the x-axis, triangle B is obtained  

On reflection in x-axis, the x-axis coordinates remain same while the y-axis coordinates become negative with the same magnitude.

Hence, the coordinates of triangle B are (4,-5),(2,-2) and (4,-2)

Now as triangle B is reflected by the line y = x to get triangle C,  the x and y coordinates of triangle B are interchanged.

So, the coordinates of triangle C are (-5,4),(-2,2) and (-2,4)

Learn more about transformation by reflection on axis:

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A.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
2
2
7
x
7
=
−
2
2
7
x
=
−
2
2
7

7x−4
7x−4+4
7x
7
7x
​
x
​
=−18
=−18+4
=−22
=
7
−22
​
=
7
−22
​
​

B.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
1
4
7
x
−
7
=
−
1
4
−
7
x
=
2

7x−4
7x−4+4
7x
−7
7x
​
x
​
=−18
=−18+4
=−14
=
−7
−14
​
=2
​

C.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
1
4
7
x
7
=
−
1
4
7
x
=
−
2

7x−4
7x−4+4
7x
7
7x
​
x
​
=−18
=−18+4
=−14
=
7
−14
​
=−2
​

D.
7
x
−
4
=
−
1
8
7
x
−
4
−
4
=
−
1
8
−
4
7
x
=
−
1
4
7
x
7
=
−
1
4
7
x
=
−
2

7x−4
7x−4−4
7x
7
7x
​
x
​
=−18
=−18−4
=−14
=
7
−14
​
=−2
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