Given points A (2,1) and B (5,1), which could be the coordinates for point C to form a triangle with area 9 square units?

To determine which coordinates for point C will create a triangle with points A (2,1) and B (5,1) that has an area of 9 square units, we can use the formula for the area of a triangle given its vertex coordinates.

The area (A) of a triangle formed by three points ((x_1, y_1)), ((x_2, y_2)), and ((x_3, y_3)) can be calculated using the formula:

[

A = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right|

]

In this case, we have points A (2,1) and B (5,1), and we are looking for a point C with coordinates ((x_C, y_C)) such that the area equals 9 square units.

Using the coordinates of points A and B and substituting into the area formula, we want:

[

9 = \frac{1}{2} \left| 2(1 - y_C) + 5