Area of triangle using coordinates

1. Write the three vertices. 2. Substitute them into the area formula. 3. Simplify the bracket carefully. 4. Take the absolute value if needed. 5. Divide by 2 and write square units.

Plot the three points in order, join them, and watch for a right triangle or easy base-height pair when the graph makes it obvious.

A common wrong answer is 12 square units because students use base times height and forget the half.

This concept finds the area of a triangle directly from the coordinates of its vertices.

This concept finds the area of a triangle directly from the coordinates of its vertices. Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. For vertices (1, 1), (5, 1), and (1, 4), the base is 4 units and the height is 3 units, so the area is 6 square units.

When base and height are not easy to see, the coordinate area formula gives a reliable answer. It uses the coordinates in a fixed order and produces area without drawing measurements by hand. The absolute value is important because area must always be non-negative. Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. For the points (1, 1), (5, 1), and (1, 4), area = 1/2 |1(1 - 4) + 5(4 - 1) + 1(1 - 1)| = 1/2 |-3 + 15 + 0| = 6 square units. Find the area of a triangle from coordinates, or use the area result to check whether points are collinear. A common wrong answer is 12 square units because students use base times height and forget the half.