Answer :
Let's clarify a couple of points first:
1. Understanding the Slope:
- The slope of a line is the ratio of the vertical change ([tex]\( \Delta y \)[/tex]) to the horizontal change ([tex]\( \Delta x \)[/tex]).
- In the problem, the slope provided is 5. This means that for every 5 units you go up vertically, you go 1 unit horizontally.
2. Right Triangles on the Line:
- A right triangle is a triangle with one 90-degree angle.
- When drawing right triangles on a line with a given slope, one of the legs of the triangle should be parallel to the x-axis (horizontal) and the other leg parallel to the y-axis (vertical).
To draw two different right triangles along a line with a slope of 5, follow these steps:
### First Right Triangle Example
1. Choose a starting point on the line (0,0):
- This will be our first vertex.
2. Determine the second vertex:
- Move horizontally by 1 unit.
- According to the slope (which is 5), move vertically by 5 units.
- This gives us the second vertex (1, 5).
3. Determine the third vertex:
- The third vertex forms a right angle with the horizontal and vertical legs.
- This vertex would be either (1, 0) or (0, 5).
- Let’s choose (1, 0) for this example.
4. Form the triangle:
- The vertices are (0,0), (1,0), and (1,5).
### Second Right Triangle Example
1. Choose a different starting point on the line (0,0):
- This will be our first vertex.
2. Determine the second vertex:
- Move horizontally by 2 units.
- According to the slope (which is 5), move vertically by 10 units (since 2 x 5 = 10).
- This gives us the second vertex (2, 10).
3. Determine the third vertex:
- The third vertex forms a right angle with the horizontal and vertical legs.
- This vertex would be either (2, 0) or (0, 10).
- Let’s choose (2, 0) for this example.
4. Form the triangle:
- The vertices are (0,0), (2,0), and (2,10).
### Graphical Representation
Here is how you would roughly visualize the two right triangles:
1. First Triangle (0,0), (1,0), (1,5):
- (0,0): Start point.
- (1,0): Move 1 unit horizontally.
- (1,5): From (1,0), move 5 units vertically.
```
(0,0) ----> (1,0)
|
|
V
(1, 5)
```
2. Second Triangle (0,0), (2,0), (2,10):
- (0,0): Start point.
- (2,0): Move 2 units horizontally.
- (2,10): From (2,0), move 10 units vertically.
```
(0,0) ------------> (2,0)
|
|
|
|
|
|
V
(2, 10)
```
By constructing these triangles, you are illustrating how different right triangles can be drawn on a line with a slope of 5. The key is that the horizontal and vertical movements must correspond to the given slope ratio.
1. Understanding the Slope:
- The slope of a line is the ratio of the vertical change ([tex]\( \Delta y \)[/tex]) to the horizontal change ([tex]\( \Delta x \)[/tex]).
- In the problem, the slope provided is 5. This means that for every 5 units you go up vertically, you go 1 unit horizontally.
2. Right Triangles on the Line:
- A right triangle is a triangle with one 90-degree angle.
- When drawing right triangles on a line with a given slope, one of the legs of the triangle should be parallel to the x-axis (horizontal) and the other leg parallel to the y-axis (vertical).
To draw two different right triangles along a line with a slope of 5, follow these steps:
### First Right Triangle Example
1. Choose a starting point on the line (0,0):
- This will be our first vertex.
2. Determine the second vertex:
- Move horizontally by 1 unit.
- According to the slope (which is 5), move vertically by 5 units.
- This gives us the second vertex (1, 5).
3. Determine the third vertex:
- The third vertex forms a right angle with the horizontal and vertical legs.
- This vertex would be either (1, 0) or (0, 5).
- Let’s choose (1, 0) for this example.
4. Form the triangle:
- The vertices are (0,0), (1,0), and (1,5).
### Second Right Triangle Example
1. Choose a different starting point on the line (0,0):
- This will be our first vertex.
2. Determine the second vertex:
- Move horizontally by 2 units.
- According to the slope (which is 5), move vertically by 10 units (since 2 x 5 = 10).
- This gives us the second vertex (2, 10).
3. Determine the third vertex:
- The third vertex forms a right angle with the horizontal and vertical legs.
- This vertex would be either (2, 0) or (0, 10).
- Let’s choose (2, 0) for this example.
4. Form the triangle:
- The vertices are (0,0), (2,0), and (2,10).
### Graphical Representation
Here is how you would roughly visualize the two right triangles:
1. First Triangle (0,0), (1,0), (1,5):
- (0,0): Start point.
- (1,0): Move 1 unit horizontally.
- (1,5): From (1,0), move 5 units vertically.
```
(0,0) ----> (1,0)
|
|
V
(1, 5)
```
2. Second Triangle (0,0), (2,0), (2,10):
- (0,0): Start point.
- (2,0): Move 2 units horizontally.
- (2,10): From (2,0), move 10 units vertically.
```
(0,0) ------------> (2,0)
|
|
|
|
|
|
V
(2, 10)
```
By constructing these triangles, you are illustrating how different right triangles can be drawn on a line with a slope of 5. The key is that the horizontal and vertical movements must correspond to the given slope ratio.
