# Transformation - Translation

## Translation - How Translation Works - Video

### Example 1

Example 1:

Here we have a pre-image, the red triangle, and the image, the yellow triangle. The pre-image is the original one, while the image is the new one.

If we count the amount of spaces from A to A', B to B', and C to C', they must be the same amount of spaces.

Since the triangle translated horizontal, we are going to count the spaces between each vertex going to left to right. In this case we have 5 spaces.

Vertex A is the point (-4, 3) and A' is the point (1, 3). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from above. Or if you subtract 1 minus -4, you will get 5.

Vertex B is the point (-4, 1) and A' is the point (1, 1). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from above. Or if you subtract 1 minus -4, you will get 5, as well.

Vertex C is the point (-1, 1) and A' is the point (4, 1). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from below. Or if you subtract 4 minus -1, you will get 5, as well.

### Example 2

Example 2:

Here we have a pre-image, the red triangle, and the image, the yellow triangle. The pre-image is the original one, while the image is the new one.

If we count the amount of spaces from A to A', B to B', and C to C', they must be the same amount of spaces.

Since the triangle translated vertically, we are going to count the spaces between each vertex going up and down. In this case we have 4 spaces.

Vertex A is the point (1, 4) and A' is the point (1, 0). If we just take a look at the y part of the points since the triangle is moving horizontally and count, we will get 4 spaces down as seen from the number line from above. Or if you subtract 4 minus 0, you will get 4.

Vertex B is the point (1, 2) and A' is the point (1, -2). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces down as seen from the number line from below. Or if you subtract 2 minus -2, you will get 4, as well.

Vertex C is the point (4, 2) and A' is the point (4, -2). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces down as seen from the number line from below. Or if you subtract 2 minus -2, you will get 5, as well.

### Example 3

Example 3:

Here we have a pre-image, the red triangle, and the image, the yellow triangle. The pre-image is the original one, while the image is the new one.

If we count the amount of spaces from A to A', B to B', and C to C', they must be the same amount of spaces.

Since the triangle translated horizontally, we are going to count the spaces between each vertex going left and right. In this case we have 5 spaces.

Vertex A is the point (-4, -1) and A' is the point (1, -1). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from above. Or if you subtract 1 minus -4, you will get 5.

Vertex B is the point (-4, -3) and A' is the point (1, -3). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from above. Or if you subtract 1 minus -4, you will get 5, as well.

Vertex C is the point (-1, -3) and A' is the point (4, -3). If we just take a look at the x part of the points since the triangle is moving horizontally and count, we will get 5 spaces to the right as seen from the number line from below. Or if you subtract 4 minus -1, you will get 5, as well.

### Example 4

Example 4:

Here we have a pre-image, the red triangle, and the image, the yellow triangle. The pre-image is the original one, while the image is the new one.

If we count the amount of spaces from A to A', B to B', and C to C', they must be the same amount of spaces.

Since the triangle translated horizontally and vertically, we are going to count the spaces between each vertex going left and right then up and down or vice versa. In this case we have 4 to the right and 1 up or 1 up and 4 to the right.

and

Vertex A is the point (-3, 3) and A' is the point (1, 4). If we just take a look at the x part of the points, first, since the triangle is moving horizontally and count, we will get 4 spaces to the right until we reach (1, 3). Or if you subtract 1 minus -3, you will get 4. Now our hand/pen is at the point (1, 3) and we move it up to (1, 4). If we subtract 4 minus 3 from the points we will get 1.

Vertex B is the point (-3, 1) and B' is the point (1, 2). If we just take a look at the x part of the points, first, since the triangle is moving horizontally and count, we will get 4 spaces to the right until we reach (1, 1). Or if you subtract 1 minus -3, you will get 4. Now our hand/pen is at the point (1, 1) and we move it up to (1, 2). If we subtract 2 minus 1 from the points we will get 1, as well.

Vertex C is the point (0, 1) and C' is the point (4, 2). If we just take a look at the x part of the points, first, since the triangle is moving horizontally and count, we will get 4 spaces to the right until we reach (4, 1). Or if you subtract 4 minus 0 you will get 4. Now our hand/pen is at the point (4, 1) and we move it up to (4, 2). If we subtract 2 minus 1 from the points we will get 1, as well.

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