Question

find the perimeter and area of triangle abc if each unit on the graph measures 1 centimeter. round answers to the nearest tenth, if necessary. a(0,9) b(4,9) c(0,1)

Explanation:

Step1: Find length of AB

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(0,9)$ and $B(4,9)$, $x_1 = 0,y_1 = 9,x_2 = 4,y_2 = 9$. Then $AB=\sqrt{(4 - 0)^2+(9 - 9)^2}=\sqrt{4^2+0^2}=4$ cm.

Step2: Find length of BC

For points $B(4,9)$ and $C(0,1)$, $x_1 = 4,y_1 = 9,x_2 = 0,y_2 = 1$. Then $BC=\sqrt{(0 - 4)^2+(1 - 9)^2}=\sqrt{(-4)^2+(-8)^2}=\sqrt{16 + 64}=\sqrt{80}\approx8.9$ cm.

Step3: Find length of AC

For points $A(0,9)$ and $C(0,1)$, $x_1 = 0,y_1 = 9,x_2 = 0,y_2 = 1$. Then $AC=\sqrt{(0 - 0)^2+(1 - 9)^2}=\sqrt{0^2+(-8)^2}=8$ cm.

Step4: Calculate perimeter

Perimeter $P=AB + BC+AC$. Substitute values: $P = 4+8.9 + 8=20.9$ cm.

Step5: Calculate area

Use formula $A=\frac{1}{2}\times base\times height$. Base $AB = 4$ cm, height (vertical distance from $C$ to $AB$) is $9 - 1=8$ cm. Then $A=\frac{1}{2}\times4\times8 = 16$ $cm^2$.

Answer:

Perimeter: $20.9$ cm, Area: $16$ $cm^2$