In Exercises 1-3, graph AABC and its image after a reflection in the given line.
1. A(0, 2), B(1, -3), C(2, 4); x-axis
1.
2. A(-2,-4), B(6,2), C(3. – 5); y-axis
3. A(4, -1), B(3, 8), C(-1, 1); y = -2

Answer:

1. Point A: (0, 2)

Point B: (-1, -3)

Point C: (-2, 4)

2. Point A: (-2, 4)

Point B: (6, -2)

Point C: (3, 5)

3. Point A: (4, -3)

Point B: (3, -12)

Point C: (-1, -5)

Step-by-step explanation:

1.

Reflection of point A:

Reflections over the x-axis are really easy. All you have to do is change the x-coordinate to the opposite sign.

In this case, 0 does not need to change since it already lies on the x-axis.

The coordinate for A will stay the same as (0, 2).

Reflection of point B:

Again, change the x-coordinate to negative.

1 → -1

The coordinate for B will now be (-1, -3).

Reflection of point C:

2 → -2

The coordinate for C will now be (-2, -4).

2.

Reflection of point A:

Reflections over the y-axis are also really easy. This time, all you have to do is change the y-coordinate to the opposite sign.

In this case, -4 would change to just 4.

The coordinate for A will stay the same as (2, 4).

Reflection of point B:

Again, change the y-coordinate to negative.

2 → -2

The coordinate for B will now be (6, -2).

Reflection of point C:

-5 → 5

The coordinate for C will now be (-1, 5).

3.

This is going to be a bit harder than the previous two, but I know you can handle it. :)

Reflection of point A:

The x will stay the same and only the y will change.

Take the y-coordinate and subtract it from the reflection line while getting the absolute value..

|(-1) - (-2)| = |1| = 1

This means, point A is one unit down the line y = -2

(-2) - 1 = -3

The coordinate for A will now be (4, -3).

Reflection of point B:

Again, the x will stay the same and only the y will change.

Using the absolute value, get the y-coordinate and subtract it from the reflection line again..

|(8) - (-2)| = |10| = 10

This means, point A is five unit down the line y = -2

(-2) - 10 = -17

The coordinate for B will now be (3, -12).

Reflection of point C:

I think you get the gist of it.

|(1) - (-2)| = |3| = 3

(-2) - 3 = -5

The coordinate for C will now be (-1, -5).

The red triangle is the original image and the blue triangle is the image after the reflection. The purple line is the reflection line.

Hope this helped!

The graph of  Exercises 1-3 that shows AABC and its image after a reflection in the given line can be done using the example from the graph attached.

A reflection over line is known to be a kind of  transformation where each point of the main or original figure (that is the pre-image) is said to be made up of an image that has similar distance from the reflection line.

Note that In a reflection, the image is said to be of similar size and also of the same shape as the original image.

Therefore to be able to construct the graph of  Exercises 1-3, one can use the image example by tracing the number values such as A(0, 2), B(1, -3), C(2, 4); x-axis, A(-2,-4), B(6,2), C(3. – 5); y-axis and  A(4, -1), B(3, 8), C(-1, 1); y = -2 on the graph and linking them up together to form an angle.

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