Question

question 1 (multiple choice worth 4 points) (04.03r mc) find the perimeter of the shape. image of a coordinate grid with a polygon labeled a, b, c, d options: 17.6, 21.4, 26.7, 32.9

Explanation:

Step1: Find coordinates of points

Assume grid has unit length. Coordinates: \(A(-4,3)\), \(B(0,2)\), \(C(2,4)\), \(D(0,-3)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For \(AB\): \(d_{AB}=\sqrt{(0 + 4)^2+(2 - 3)^2}=\sqrt{16 + 1}=\sqrt{17}\approx4.12\)
For \(BC\): \(d_{BC}=\sqrt{(2 - 0)^2+(4 - 2)^2}=\sqrt{4 + 4}=\sqrt{8}\approx2.83\)
For \(CD\): \(d_{CD}=\sqrt{(0 - 2)^2+(-3 - 4)^2}=\sqrt{4 + 49}=\sqrt{53}\approx7.28\)
For \(DA\): \(d_{DA}=\sqrt{(0 + 4)^2+(-3 - 3)^2}=\sqrt{16 + 36}=\sqrt{52}\approx7.21\)

Step3: Sum distances for perimeter

\(P\approx4.12+2.83+7.28+7.21 = 21.44\approx21.4\)

Answer:

21.4