# Common Core: High School - Geometry : Congruence

## Example Questions

### Example Question #3 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , , , and  and after a transformation results in the coordinates , , , and  identify the transformation.

Reflection

Rotation

Dilation

Extension

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

### Example Question #4 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Rotation

Dilation

Translation

Reflection

Translation

Explanation:

To identify the transformation that is occurring in this particular problem, recall the different transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Looking at the starting and ending coordinates of the rectangle,

, and   to  , and

Since all the  coordinates are increasing by two this is known as a translation.

### Example Question #5 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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 #6 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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 #7 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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 #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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 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 #9 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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

### Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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 #51 : High School: Geometry

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 #12 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

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?