# How do you find the area of the right triangle ABC with A= (-2,7), B= (7,-1), C= (3,9)?

##### 1 Answer

Jun 5, 2015

ABC (with the given coordinates) is **not** a right triangle.

The area of the triangle can be evaluated by:

- Determining the lengths of
#|AB|, |BC|, and |AC|#

#color(white)("XXXX")# Square Root of (#(Delta x)^2 + (Delta y)^2)# ) - Determining the perimeter and semi-perimeter

#color(white)("XXXX")# #p =# sum of#|AB| + |BC| + |AC|#

#color(white)("XXXX")# #s= p/2# - Applying Heron's formula

#color(white)("XXXX")# A=#sqrt(s(s-a)(s-b)(s-c))#

The image below shows the results with the arithmetic details handled by a spreadsheet.