Question

graph the following figure in the coordinate plane. find the perimeter. a(1,1), b(7,9), c(7,0) choose the correct graph on the right. the perimeter of δabc is \\(\square\\) units. (type an exact answer, using radicals as needed.)

Explanation:

Step1: Find length of BC

Points B(7,9) and C(7,0). Since x - coordinates are same, length is \( |9 - 0| = 9 \).

Step2: Find length of AC

Points A(1,1) and C(7,0). Use distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
\( d=\sqrt{(7 - 1)^2+(0 - 1)^2}=\sqrt{36 + 1}=\sqrt{37} \).

Step3: Find length of AB

Points A(1,1) and B(7,9). Use distance formula.
\( d=\sqrt{(7 - 1)^2+(9 - 1)^2}=\sqrt{36 + 64}=\sqrt{100}=10 \).

Step4: Calculate perimeter

Perimeter = AB + BC + AC = \( 10 + 9 + \sqrt{37}=19+\sqrt{37} \).

Answer:

\( 19 + \sqrt{37} \)