Question

coordinate geometry coordinate geometry unit test (0,5) (4,5) (4,0) what is the perimeter of the triangle rounded to the nearest tenth of a unit? what is the area of the

Explanation:

Perimeter Calculation

Step1: Identify side lengths

• Horizontal side: Distance between \((0,5)\) and \((4,5)\). Since \(y\)-coordinates are same, length is \(|4 - 0| = 4\).
• Vertical side: Distance between \((4,5)\) and \((4,0)\). Since \(x\)-coordinates are same, length is \(|5 - 0| = 5\).
• Hypotenuse: Distance between \((0,5)\) and \((4,0)\). Use distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). So \(d=\sqrt{(4 - 0)^2+(0 - 5)^2}=\sqrt{16 + 25}=\sqrt{41}\approx6.4\).

Step2: Sum the sides

Perimeter \(= 4 + 5 + \sqrt{41}\approx4 + 5 + 6.4 = 15.4\).

Area Calculation

Step1: Identify base and height

• Base (horizontal side) \(= 4\), height (vertical side) \(= 5\).

Step2: Apply triangle area formula

Area \(=\frac{1}{2}\times\text{base}\times\text{height}=\frac{1}{2}\times4\times5 = 10\).

Answer:

(Perimeter):
\(15.4\) units