Final answer:
To find the perimeter of a triangle with vertices A(-6,-3), B(1,-1), C(1,-5), use the distance formula to find the lengths of all three sides, and then add them together. The perimeter of the triangle is approximately 11.57 units.
Step-by-step explanation:
To find the perimeter of a triangle, you need to find the length of all three sides and then add them together. Let's start by finding the length of side AB using the distance formula.
AB = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(1 - (-6))^2 + (-1 - (-3))^2] = √[7^2 + 2^2]
= √[49 + 4] = √53.
Now, find the length of side BC: BC = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(1 - 1)^2 + (-5 - (-1))^2]
= √[0^2 + (-4)^2]
= √16 = 4.
Finally, find the length of side CA: CA = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(-6 - 1)^2 + (-3 - (-5))^2]
= √[-7^2 + 2^2]
= √[49 + 4]
= √53.
Now, add all three side lengths together to get the perimeter: AB + BC + CA = √53 + 4 + √53
≈ 11.57.
So, the perimeter of the triangle is approximately 11.57 units.