All Common Core: High School - Geometry Resources
Example Questions
Example Question #575 : 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?
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 #576 : High School: Geometry
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?
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 #577 : High School: Geometry
The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?
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 #1 : 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?
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
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