Archaeologists attempt to reconstruct past ways of life by examining preserved bones, the ruins of buildings, and artifacts such as tools, p

A = (-1, 6)         B = (4, 5)         C = (-3, -4)

Use the distance formula to find the distance of each side:  d  =  √[ (x2 - x1)² + (y2 - y1)² ]

AB:  (x1, y1) = (-1, 6)         (x2, y2) = (4, 5)     --->  d  =  √[ (4 - -1)² + (5 - 6)² ]  

       --->   d  =  √[ (5)² + (-1)² ]     --->   d  =  √( 25 + 1)     --->     d  =  √26

BC:  (x1, y1) = (4, 5)         (x2, y2) = (-3, -4)     --->  d  =  √[ (-3 - 4)² + (-4 - 5)² ]  

       --->   d  =  √[ (-7)² + (-9)² ]     --->   d  =  √( 49 + 81)     --->     d  =  √130

AC:  (x1, y1) = (-1, 6)         (x2, y2) = (-3, -4)     --->  d  =  √[ (-3 - -1)² + (-4 - 6)² ]  

       --->   d  =  √[ (-2)² + (-10)² ]     --->   d  =  √( 4 + 100)     --->     d  =  √104

Since AB² + AC²  =  BC², this is a right triangle with sides AB and AC.

To find the area:  Area  =  ½ · AB · AC  =  ½ · √26 · √104 =  ½ · √2704  =  ½ · 52  =  26