Question

3 find the perimeter of the shape in the coordinate plane. round to the nearest hundredth. coordinates of point a: (-3, 2) coordinates of point b: (2, -1) coordinates of point c: (2, 1) ab = 5

Explanation:

Step1: Identify coordinates

Point A: \((-3, 2)\), Point B: \((2, -1)\), Point C: \((2, 1)\)

Step2: Calculate AB length

Use distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
\(AB = \sqrt{(2 - (-3))^2 + (-1 - 2)^2} = \sqrt{5^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83\)

Step3: Calculate BC length

\(BC = \sqrt{(2 - 2)^2 + (1 - (-1))^2} = \sqrt{0 + 4} = 2\)

Step4: Calculate AC length

\(AC = \sqrt{(2 - (-3))^2 + (1 - 2)^2} = \sqrt{5^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26} \approx 5.10\)

Step5: Sum lengths for perimeter

Perimeter = \(AB + BC + AC \approx 5.83 + 2 + 5.10 = 12.93\)

Answer:

The perimeter of the shape is approximately \(\boldsymbol{12.93}\).