Question

coordinate geometry coordinate proofs use the given coordinates to compute the perimeter of the parallelogram. (1 point) 29 units 21.9 units 20.9 units 10.5 units

Explanation:

Step1: Calculate the length of \( AT \)

The formula for the distance 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 points \(A(-2,2)\) and \(T(4,2)\), \(y_1 = y_2=2\). Then \(AT=\sqrt{(4-(-2))^2+(2 - 2)^2}=\sqrt{(6)^2+0}=6\)

Step2: Calculate the length of \( AM \)

For points \(A(-2,2)\) and \(M(-4,-2)\), use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-2,y_1 = 2,x_2=-4,y_2=-2\). Then \(AM=\sqrt{(-4 + 2)^2+(-2 - 2)^2}=\sqrt{(-2)^2+(-4)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47\)

Step3: Use the perimeter formula of a parallelogram

The perimeter formula of a parallelogram \(P = 2(a + b)\), where \(a\) and \(b\) are the side - lengths of the parallelogram. Here \(a = AT=6\) and \(b = AM\approx4.47\). Then \(P=2(6 + 4.47)=2\times10.47 = 20.94\approx20.9\)

Answer:

20.9 units