A rectangle with a vertex at (8,-2) is translated 3 units down. What are the coordinates of this vertex after it is translated? Draw a graph if necessary.
To translate a figure down, we subtract the same value from the y-coordinates of all its vertices. In this case, we subtract 3 units from the y-coordinate of the vertex (8, -2).
The new y-coordinate is calculated as:
-2 - 3 = -5
So the vertex moves from (8, -2) to (8, -5).
Graphically, the original vertex (8, -2) is shown below:
<img src="https://latex.codecogs.com/svg.latex?\Large&space;\begin{align*}&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&space;\\&space;&space;&space;&&space;&&space;\bullet&space;&&space;&&space;&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;\\&space;&&space;&&space;&&space;&&space&&space;\\&space;\end{align*}}" title="\Large \begin{align*} && && && && && && && && && && && && && && && && && && && && && && \\ && && \bullet && && && && && && && && && && && && && && \\ && && && && &&&& \\ \end{align*}}" />
After translating 3 units down, the new vertex is (8, -5):
<img src="https://latex.codecogs.com/svg.latex?\Large&space;\begin{align*}&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&space;\\&space;&space;&space;&&space;&&space;\bullet&space;&&space;&&space;&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;&&space;\\&space;&&space;&&space;&&space;&&space&&space;\\&space;\end{align*}}" title="\Large \begin{align*} && && && && && && && && && && && && && && && && && && && && && && \\ && && \bullet && && && && && && && && && && && && && && && \\ && && && && &&&& \\ \end{align*}}" />
To translate the rectangle 3 units down, we need to subtract 3 from the y-coordinate of the vertex.
Given the vertex (8, -2), subtracting 3 from the y-coordinate gives us:
New y-coordinate = -2 - 3 = -5
So, the coordinates of the vertex after it is translated 3 units down are (8, -5).
To visualize this translation, let's draw a graph:
Graph:
|
---|-------
|
|
|
|
|
|
‾‾‾‾‾‾‾‾‾