# Common Core: High School - Geometry : Draw specific transformed figures

## Example Questions

### Example Question #1 : Draw Specific Transformed Figures

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #2 : Draw Specific Transformed Figures

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the -axis take the opposite of all the  values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #3 : Draw Specific Transformed Figures

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the  and -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #4 : Draw Specific Transformed Figures

The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the reflected triangle has coordinates at

### Example Question #5 : Draw Specific Transformed Figures

A rectangle's coordinate points are , , , and . If the rectangle is translated down seven units what are the coordinates of the translated rectangle?

Explanation:

To find the coordinates of the translated rectangle, first recall what a translation is. A translation is a shift of the original object without changing the shape of size of the object. In this particular case the starting coordinates of the rectangle are given and the goal is to move the rectangle down seven units. A shift down means a algebraic change in the  coordinate.

The original rectangle is

If each point on the rectangle is shifted down seven units it results in the following

Therefore, the coordinate points of the translated rectangle are

These coordinates can also be found algebraically by subtracting seven from each  value.

### Example Question #6 : Draw Specific Transformed Figures

A rectangle's coordinate points are , , , and . If the rectangle is translated up  units and to the right  units what are the coordinates of the translated rectangle?

Explanation:

To find the coordinates of the translated rectangle, first recall what a translation is. A translation is a shift of the original object without changing the shape of size of the object. In this particular case the starting coordinates of the rectangle are given and the goal is to move the rectangle up two units and to the right 5 units. A shift up means a algebraic change in the  coordinate and a shift to the right means an algebraic change to the  coordinate.

The original rectangle is

If each point on the rectangle is shifted up two units and to the right five units results in the following

Therefore, the coordinate points of the translated rectangle are

### Example Question #7 : Draw Specific Transformed Figures

The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the reflected triangle has coordinates at

### Example Question #8 : Draw Specific Transformed Figures

The coordinates of a triangle are , , and . What are the coordinates of this triangle after it is reflected across the  and -axis?