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.