Part A: Find the length of each side of the triangle. Show your work. (4 points) Part B: Find the slope of each side of the triangle. Show your work (3 points)

To find the length of each side of the triangle, you can use the distance formula, which is given by the formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Suppose the coordinates of the vertices of the triangle are A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). You would calculate \(AB\), \(BC\), and \(CA\) using the distance formula. For example, if A(1,2), B(4,6), and C(7,2), then the length of side AB would be: \[ AB = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] You would apply this method to find all three sides. To find the slope of each side of the triangle, you can use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Continuing with the same points A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃), you'd calculate the slopes of AB, BC, and CA. For instance, to find the slope of AB, it would be: \[ m_{AB} = \frac{6-2}{4-1} = \frac{4}{3} \] Using this formula, you would do the same calculation for the other sides to find their respective slopes.