Question

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

Answer 1

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

The area of the triangle can be evaluated by:

1. Determining the lengths of `|AB|, |BC|, and |AC|`
   `color(white)("XXXX")`Square Root of (`(Delta x)^2 + (Delta y)^2)`)
2. Determining the perimeter and semi-perimeter
   `color(white)("XXXX")` `p =` sum of `|AB| + |BC| + |AC|`
   `color(white)("XXXX")` `s= p/2`
3. 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.