Q. Find the perimeter of the triangle whose vertices are (−2,−1),(1,−1), and (1,3). Write the exact answer. Do not round.Answer
Calculate Distance Between Vertices: Calculate the distance between the first two vertices (−2,−1) and (1,−1). Use the distance formula: d=((x2−x1)2+(y2−y1)2). Here, (x1,y1)=(−2,−1) and (x2,y2)=(1,−1). d=((1−(−2))2+(−1−(−1))2)=((1+2)2+(0)2)=(32+0)=9=3.
Calculate Distance Between Vertices: Calculate the distance between the second and third vertices (1,−1) and (1,3). Use the distance formula: d=(x2−x1)2+(y2−y1)2. Here, (x1,y1)=(1,−1) and (x2,y2)=(1,3). d=(1−1)2+(3−(−1))2=(0)2+(3+1)2=0+42=16=4.
Calculate Distance Between Vertices: Calculate the distance between the third vertex (1,3) and the first vertex (−2,−1). Use the distance formula: d=((x2−x1)2+(y2−y1)2). Here, (x1,y1)=(1,3) and (x2,y2)=(−2,−1). d=((−2−1)2+(−1−3)2)=((−3)2+(−4)2)=(9+16)=25=5.
Find Perimeter of Triangle: Add the distances from steps 1, 2, and 3 to find the perimeter of the triangle.Perimeter = side1+side2+side3=3+4+5=12.