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find leg 1 and leg 2 with the distance as well

To find the legs and hypotenuse of the right triangle formed by the points \( (-7, 4) \) and \( (-4, -1) \), we can follow these steps:

1. **Leg 1 (Horizontal Distance)**:
   The horizontal distance is the difference in the x-coordinates of the two points. This forms one leg of the right triangle.
   \[
   \text{Leg 1} = |x_2 - x_1| = |-4 - (-7)| = |-4 + 7| = 3
   \]

2. **Leg 2 (Vertical Distance)**:
   The vertical distance is the difference in the y-coordinates of the two points. This forms the other leg of the right triangle.
   \[
   \text{Leg 2} = |y_2 - y_1| = |-1 - 4| = |-5| = 5
   \]

3. **Hypotenuse (Distance between the two points)**:
   The hypotenuse is the distance between the two points, which can be found using the Pythagorean theorem:
   \[
   d = \sqrt{(\text{Leg 1})^2 + (\text{Leg 2})^2} = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.83
   \]

Thus, the two legs of the triangle are 3 and 5, and the distance (hypotenuse) is approximately 5.83 units.

Would you like further clarification or additional details?

Here are some related questions:
1. How can we determine the midpoint of a line segment between two points?
2. What is the formula for finding the slope of a line given two points?
3. How do you use the distance formula in 3D geometry?
4. What are the properties of a right triangle in terms of angles?
5. How can you calculate the area of a triangle given its base and height?

**Tip:** Always visualize the points on a graph if possible. This can help you better understand the geometry and distances involved.

Learn how to find the legs and hypotenuse of a right triangle formed by points (-7, 4) and (-4, -1) using the distance formula and Pythagorean theorem. Discover detailed steps and calculations with an example. Suitable for Grades 7-9 students.

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