Question

Perimeter =
units
Plot and connect the points in the order listed below. When you are done, find the perimeter of the resulting figure.
A, left parenthesis, minus, 4, comma, 3, right parenthesisA(−4,3), B, left parenthesis, 1, comma, 3, right parenthesisB(1,3), C, left parenthesis, 1, comma, minus, 2, right parenthesisC(1,−2), D, left parenthesis, minus, 4, comma, minus, 2, right parenthesisD(−4,−2)

Answer 1

To find the perimeter of the figure formed by the points A(-4, 3), B(1, 3), C(1, -2), and D(-4, -2), we first need to determine the lengths of the sides connecting these points.

1. **Distance AB**:
- Coordinates: A(-4, 3) and B(1, 3)
- Distance \( AB = \sqrt{(1 - (-4))^2 + (3 - 3)^2} = \sqrt{(1 + 4)^2 + 0^2} = \sqrt{5^2} = 5 \)

2. **Distance BC**:
- Coordinates: B(1, 3) and C(1, -2)
- Distance \( BC = \sqrt{(1 - 1)^2 + (-2 - 3)^2} = \sqrt{0^2 + (-5)^2} = \sqrt{25} = 5 \)

3. **Distance CD**:
- Coordinates: C(1, -2) and D(-4, -2)
- Distance \( CD = \sqrt{(-4 - 1)^2 + (-2 - (-2))^2} = \sqrt{(-5)^2 + 0^2} = \sqrt{25} = 5 \)

4. **Distance DA**:
- Coordinates: D(-4, -2) and A(-4, 3)
- Distance \( DA = \sqrt{(-4 - (-4))^2 + (3 - (-2))^2} = \sqrt{0^2 + (3 + 2)^2} = \sqrt{5^2} = 5 \)

Now that we have the lengths of all sides, we can calculate the perimeter:

\[
\text{Perimeter} = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20 \text{ units}
\]

Thus, the perimeter of the resulting figure is **20 units**.