Triangl XYZ with X = (3,7) Y = (-1,-5) Z = (6,-4) The three sides are created by the line segment XY, the line segment XZ, and the line segment YZ.We need the lengths of these three line segments which will be the distance from x to y, x to z, and y to z.We need to find the 3 distances and then add them together. The distance between two points is found from the distance formulad = √((x2-x1)2+(y2-y1)2) XY = √((-1-3)2+(-5-7)2) = √((-4)2+(-12)2) = √(16 + 144) = √(160) = 4√10 xz = √((6-3)2+(-4-7)2) = √(32 + (-11)2) = √(9+121) = √130 yz = √(((6-(-1))2+(-4-(-5))2) = √(72 +12) = √50 = 5√2 We now have the lengths of each side of the triangle so add them to find perimeter P = 4√10 + √130 + 5√2 ≅ 31.122
