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

Jun 5, 2015

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

The area of the triangle can be evaluated by:

1. Determining the lengths of $| A B | , | B C | , \mathmr{and} | A C |$
$\textcolor{w h i t e}{\text{XXXX}}$Square Root of ((Delta x)^2 + (Delta y)^2))
2. Determining the perimeter and semi-perimeter
$\textcolor{w h i t e}{\text{XXXX}}$$p =$ sum of $| A B | + | B C | + | A C |$
$\textcolor{w h i t e}{\text{XXXX}}$$s = \frac{p}{2}$
3. Applying Heron's formula
$\textcolor{w h i t e}{\text{XXXX}}$A= $\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

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