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

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

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

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

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.

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

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

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  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original triangle 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 triangle are

In order to construct a  angle using a ray, first recall what a  angle and ray are.

An angle in the most basic terms is when two rays having the same vertex, are going in different directions.

Now, recall that a  angle occurs when the lines or rays of the angle intersect perpendicularly.

Since the problem gives the starting ray,

which is a horizontal ray, then to create a  angle, a vertical ray needs to be constructed from the same vertex. To identify a  angle it is common practice to draw a square at the vertex to show the angle measurement. This results in the final solution.

To identify the first step that must be taken when constructing a parallel line, there is some information about the given line that needs to be clearly established first.

First recall what it means to be parallel. For lines to be parallel, their slopes must be equal and they must have different  and  intercepts. If two lines have the same intercepts and the same slope they are not parallel lines, they are the same line. Parallel lines mean that two lines will never intersect.

From here, look at the possible answers to decide which one is best.

"Identify the two lines intersection point." by definition of parallel lines this is false since parallel lines never intersect.

"Find the -intercept of the given line." and "Find the -intercept of the given line." could possible be considered among the steps to constructing parallel lines but not necessarily.

"Take the negative reciprocal of the given line's slope." Taking this would give the slope of a perpendicular line.

"Calculate the slope of the given line." in order to construct a parallel line, the slope must first be calculated on the given line. Therefore, this is the best answer.