Questions: Find the perimeter of triangle ABC with vertices A(1, 1), B(7,1), and C(1,9). Select one: a. 114 units b. 14 units c. 28 units d. 24 units

Solution Steps

The vertices of the triangle are given as:

• A(1, 1)
• B(7, 1)
• C(1, 9)

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

\[ AB = \sqrt{(7 - 1)^2 + (1 - 1)^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6 \]

\[ BC = \sqrt{(1 - 7)^2 + (9 - 1)^2} = \sqrt{(-6)^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]

\[ CA = \sqrt{(1 - 1)^2 + (9 - 1)^2} = \sqrt{0^2 + 8^2} = \sqrt{64} = 8 \]

\[ \text{Perimeter} = AB + BC + CA = 6 + 10 + 8 = 24 \]

Final Answer