Final answer:
The area of the triangle is calculated using the base and height obtained from the line's x-intercept and the y-axis intersection. After solving, the area calculation gives 25 square units, but this is not an option in the provided choices, indicating the need to re-evaluate the triangle's vertices.
Step-by-step explanation:
We are asked to find the area of a triangle bounded by the y-axis, the line f(x) = 10 - 2x, and the line perpendicular to f(x) that passes through the origin. First, let's find the x-intercept of the line f(x) by setting f(x) = 0 and solving for x, which gives us x = 5. This point (5,0) is one vertex of the triangle. The other two vertices are (0,0) and (0,10), since the line crosses the y-axis at y = 10.
The slope of the line f(x) is -2, so the slope of the perpendicular line would be 1/2 (perpendicular lines have slopes that are negative reciprocals). The y-intercept of this perpendicular line is 0, so the line equation is y = 1/2x. However, because we are finding the area bounded by the y-axis, the perpendicular line's equation is not needed to calculate the triangle's area.
Since we have the base and height of the right triangle (base = 5, height = 10), we can now use the formula for the area of a right triangle, area = (base * height) / 2. Therefore, the area = (5 * 10) / 2 = 25 square units.
This calculation does not match any of the provided options (A, B, C, D), so we need to verify that the origin is indeed a vertex of the triangle, as initially assumed. If not, we have not identified the correct vertices and thus have an incorrect base or height for our triangle.