Final answer:
The area of a triangle formed by the coordinate axes and a line through (2,1) is given by the formula 1/2 × base × height, which simplifies to 1/2 × x, matching option 1) from the provided choices.
Step-by-step explanation:
The question is asking for the area of a triangle formed by the two coordinate axes and a line passing through the point (2,1). To find the area of such a triangle, we recall the formula for the area of a triangle, which is 1/2 × base × height.
Since the triangle in question is formed by the coordinate axes, its base and height correspond to the x and y coordinates of the point through which the line passes. Therefore, if we consider the length x to be the length along the x-axis (which is 2 in this case), then the base of the triangle is x, and the height is the y-coordinate (which is 1 in this case).
Applying the formula, the area A = 1/2 × base × height = 1/2 × x × 1. Among the choices provided, this simplifies to 1/2 × x, which corresponds to option 1).