Plot the points (2,4), (-1,4) and (2,1) and connect them to form a triangle. What rule would you use to translate the triangle 5 units to the right? Write your rule in the form H(x,y) = (?,?). Draw the translated figure and label its coordinates.
7,2
To plot the points (2,4), (-1,4), and (2,1), you will need to locate them on a graph. The first number in each coordinate pair represents the x-coordinate, and the second number represents the y-coordinate.
To draw the triangle, locate each point on the graph and connect them with straight lines. It will look like this:
```
(2,1)
*
|\
| \
| \
| \
| \
*-----*
(2,4) (-1,4)
```
To translate the triangle 5 units to the right, you will need to add 5 to each x-coordinate. The general rule for translating a point (x, y) to the right by a distance of 'a' units is: H(x, y) = (x + a, y).
In this case, you want to translate each point 5 units to the right. So, applying the translation rule to each of the original points:
- (2, 4) translates to (2 + 5, 4) = (7, 4)
- (-1, 4) translates to (-1 + 5, 4) = (4, 4)
- (2, 1) translates to (2 + 5, 1) = (7, 1)
Now, plot the translated points on a new graph:
```
(7,1)
*
|\
| \
| \
| \
| \
*-----*
(7,4) (4,4)
```
This is your translated triangle. The coordinates for the translated points are (7, 4), (4, 4), and (7, 1).