Question

1. find the perimeter of quadrilateral rstu. round to the nearest tenth if necessary. r(-3, 3), s(0, 1), t(5, 3), u(-3, -5)

Explanation:

Step1: Recall Distance Formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Also, if two points have the same \(x\)-coordinate (vertical line) or same \(y\)-coordinate (horizontal line), the distance is \(|y_2 - y_1|\) or \(|x_2 - x_1|\) respectively.

Step2: Find \(RS\)

Points \(R(-3, 3)\) and \(S(0, 1)\).
Using distance formula: \(RS=\sqrt{(0 - (-3))^2 + (1 - 3)^2}=\sqrt{(3)^2 + (-2)^2}=\sqrt{9 + 4}=\sqrt{13}\approx 3.6\)

Step3: Find \(ST\)

Points \(S(0, 1)\) and \(T(5, 3)\).
Using distance formula: \(ST=\sqrt{(5 - 0)^2 + (3 - 1)^2}=\sqrt{25 + 4}=\sqrt{29}\approx 5.4\)

Step4: Find \(TU\)

Points \(T(5, 3)\) and \(U(-3, -5)\).
Using distance formula: \(TU=\sqrt{(-3 - 5)^2 + (-5 - 3)^2}=\sqrt{(-8)^2 + (-8)^2}=\sqrt{64 + 64}=\sqrt{128}\approx 11.3\)

Step5: Find \(UR\)

Points \(U(-3, -5)\) and \(R(-3, 3)\).
Since \(x\)-coordinates are same, distance is \(|3 - (-5)| = |8| = 8\)

Step6: Calculate Perimeter

Perimeter \(= RS + ST + TU + UR\approx 3.6 + 5.4 + 11.3 + 8 = 28.3\)

Answer:

\(28.3\)