Question

Q (1,6)
P (1,2)
R (-4,2)

Use the given coordinates to compute the perimeter of the triangle. Round your answer to the nearest tenth

The perimeter is approximately __ units

Answer 1

To find the perimeter of the triangle formed by the points Q(1, 6), P(1, 2), and R(-4, 2), we need to calculate the lengths of the three sides of the triangle.

1. **Find the distance between points Q and P:**

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- For Q(1, 6) and P(1, 2):
\[
d_{QP} = \sqrt{(1 - 1)^2 + (2 - 6)^2} = \sqrt{0 + (-4)^2} = \sqrt{16} = 4
\]

2. **Find the distance between points P and R:**
- For P(1, 2) and R(-4, 2):
\[
d_{PR} = \sqrt{(-4 - 1)^2 + (2 - 2)^2} = \sqrt{(-5)^2 + 0} = \sqrt{25} = 5
\]

3. **Find the distance between points Q and R:**
- For Q(1, 6) and R(-4, 2):
\[
d_{QR} = \sqrt{(-4 - 1)^2 + (2 - 6)^2} = \sqrt{(-5)^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41}
\]

4. **Calculate \(\sqrt{41}\):**
- Approximately, \(\sqrt{41} \approx 6.4\) (using a calculator or estimation).

5. **Calculate the perimeter of the triangle:**
\[
\text{Perimeter} = d_{QP} + d_{PR} + d_{QR} = 4 + 5 + 6.4 = 15.4
\]

Thus, the perimeter of the triangle is approximately **15.4 units**.