Questions: Find the perimeter of the triangle whose vertices are the following specified points in the plane. (-4,-2),(-3,-5) and (3,-7)

Solution Steps

Using the distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\), we find:

• Distance between \((x_1, y_1)\) and \((x_2, y_2)\): \(d_{12} = \sqrt{(-3 + 4)^2 + (-5 + 2)^2} = 3.16\)
• Distance between \((x_2, y_2)\) and \((x_3, y_3)\): \(d_{23} = \sqrt{(3 + 3)^2 + (-7 + 5)^2} = 6.32\)
• Distance between \((x_3, y_3)\) and \((x_1, y_1)\): \(d_{31} = \sqrt{(-4 - 3)^2 + (-2 + 7)^2} = 8.6\)

The perimeter of the triangle is the sum of these distances: \(Perimeter = d_{12} + d_{23} + d_{31} = 3.16 + 6.32 + 8.6 = 18.09\)

Final Answer: