# Coordinate Geometry-9

### From Homeworkwiki

**Find the area of the triangle joining the points (1, -3), (3, 1), (1, 4)**

**Solution:** Let (x_{1}, y_{1}) = (1, -3); (x_{2}, y_{2}) = (3, 1); (x_{3}, y_{3}) = (1, 4)

Area of Triangle = 1/2 [ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) ]

= 1/2 [1(1 - 4) + 3(4 + 3) + 1(-3 - 1)]

= 1/2 (-3 + 21 - 4) = 1/2 (14) = 7 square units.