Question

Given triangle JKL on the coordinate plane.

Point J is at (1, 7)

Point K is at (6, 1)

Point L is at (1, 1)

(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The length of side JK is Response area

The length of side LK is Response area.

The length of side JL is Response area.

The perimeter of triangle JKL in simplest radical form Response area.

Answer 1

Let's calculate the lengths of the sides of triangle JKL first.

1. **Length of side JK**:
Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
For points J(1, 7) and K(6, 1):
\[
JK = \sqrt{(6 - 1)^2 + (1 - 7)^2} = \sqrt{(5)^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61}
\]

2. **Length of side LK**:
For points L(1, 1) and K(6, 1):
\[
LK = \sqrt{(6 - 1)^2 + (1 - 1)^2} = \sqrt{(5)^2 + (0)^2} = \sqrt{25} = 5
\]

3. **Length of side JL**:
For points J(1, 7) and L(1, 1):
\[
JL = \sqrt{(1 - 1)^2 + (1 - 7)^2} = \sqrt{(0)^2 + (-6)^2} = \sqrt{36} = 6
\]

Now, we can find the perimeter of triangle JKL:

\[
\text{Perimeter} = JK + LK + JL = \sqrt{61} + 5 + 6
\]

Thus, the perimeter is:

\[
\text{Perimeter} = \sqrt{61} + 11
\]

Now let's put together the responses for the question:

- The length of side JK is **√61**.
- The length of side LK is **5**.
- The length of side JL is **6**.
- The perimeter of triangle JKL in simplest radical form is **√61 + 11**.