Final answer:
To find the point of intersection, the slope of the given line is calculated then used to determine the perpendicular line's equation. The two equations are set equal to solve for x, then substituted back to find y, revealing the intersection point as (8, 1).
Step-by-step explanation:
To calculate the point of intersection for a line and another line that is perpendicular to it and passes through a given point, we must first find the slope of the perpendicular line. The slope of the given line, 2x - 4y = 12, is 1/2 since rearranging it to slope-intercept form, y = (1/2)x - 3, reveals this slope. The slope of a line perpendicular to it will be the negative reciprocal, thus, the slope of the perpendicular line is -2.
Next, we use the point (7, 3) to determine the equation of the perpendicular line. The point-slope form of this line's equation is y - 3 = -2(x - 7). Simplifying, we have y = -2x + 17.
Finally, to find the point of intersection, we set the y-values of both lines equal and solve for x. Thus, (1/2)x - 3 = -2x + 17, which simplifies to (5/2)x = 20, so . Plugging into one of the line equations, y = -2(8) + 17 = 1, yields the point of intersection as (8, 1).