Question
The coordinates of the vertices of △JKL are J(−5, −1), K(0, 1), and L(2, −5).

Which statement correctly describes whether △JKL is a right triangle?

Responses

△JKL is a right triangle because JL¯¯¯¯¯ is perpendicular to KL¯¯¯¯¯.
triangle J K L is a right triangle because segment J L is perpendicular to segment K L .

△JKL is a right triangle because JK¯¯¯¯¯ is perpendicular to KL¯¯¯¯¯.
triangle J K L is a right triangle because segment J K is perpendicular to segment K L .

△JKL is a right triangle because JK¯¯¯¯¯ is perpendicular to JL¯¯¯¯¯.
triangle J K L is a right triangle because segment J K is perpendicular to segment J L .

△JKL is not a right triangle because no two of its sides are perpendicular.

To determine if △JKL is a right triangle, we need to check if any two of its sides are perpendicular by comparing their slopes. If two sides are perpendicular, the product of their slopes should equal -1.

### Step 1: Find the slopes of each side
1. **Slope of \( JK \)**:
   \[
   \text{slope}_{JK} = \frac{1 - (-1)}{0 - (-5)} = \frac{1 + 1}{5} = \frac{2}{5}
   \]

2. **Slope of \( JL \)**:
   \[
   \text{slope}_{JL} = \frac{-5 - (-1)}{2 - (-5)} = \frac{-5 + 1}{2 + 5} = \frac{-4}{7}
   \]

3. **Slope of \( KL \)**:
   \[
   \text{slope}_{KL} = \frac{-5 - 1}{2 - 0} = \frac{-6}{2} = -3
   \]

### Step 2: Check for perpendicularity
- The slopes of \( JK \) and \( JL \) are \(\frac{2}{5}\) and \(-\frac{4}{7}\), respectively. Their product is:
  \[
  \frac{2}{5} \times -\frac{4}{7} = -\frac{8}{35} \neq -1
  \]
  So, \( JK \) and \( JL \) are not perpendicular.

- The slopes of \( JK \) and \( KL \) are \(\frac{2}{5}\) and \(-3\), respectively. Their product is:
  \[
  \frac{2}{5} \times -3 = -\frac{6}{5} \neq -1
  \]
  So, \( JK \) and \( KL \) are not perpendicular.

- The slopes of \( JL \) and \( KL \) are \(-\frac{4}{7}\) and \(-3\), respectively. Their product is:
  \[
  -\frac{4}{7} \times -3 = \frac{12}{7} \neq -1
  \]
  So, \( JL \) and \( KL \) are not perpendicular.

### Conclusion
Since no two sides of △JKL are perpendicular, the triangle is **not a right triangle**.

The correct answer is:
- **△JKL is not a right triangle because no two of its sides are perpendicular.**

Would you like more details or have questions? 

Here are some related questions:
1. How can we use the distance formula to check the side lengths in triangles?
2. Why does the product of slopes being -1 imply perpendicularity?
3. How do we determine the type of triangle based on its angles?
4. What are some ways to classify triangles other than angle-based classification?
5. How can we determine the area of a triangle given its vertices?

**Tip:** Always check for perpendicular slopes when trying to identify right triangles in coordinate geometry.

The coordinates of the vertices of △JKL are J(−5, −1), K(0, 1), and L(2, −5). Which statement correctly describes whether △JKL is a right triangle?

Explore whether △JKL, with vertices at J(−5, −1), K(0, 1), and L(2, −5), forms a right triangle. This problem involves calculating slopes and applying the perpendicularity condition, perfect for Grades 8-10 students learning coordinate geometry.

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