Which point is on the line that passes through point H and is perpendicular to line FG?
(-6,10)
(-2,-12)
(0,-2)
(4,2)
Answer (2)
Without the coordinates of points F, G, and H, it is impossible to determine the line perpendicular to FG that passes through H, and thus impossible to identify which of the given points lies on that line.
Explanation
Problem Analysis The problem asks us to identify a point that lies on a line perpendicular to line FG and passing through point H. However, the coordinates of points F, G, and H are not provided. Therefore, we cannot determine the equation of the line and cannot identify which of the given points lies on it.
Impossibility of Solution Since we lack the coordinates for points F, G, and H, we cannot compute the slope of line FG, nor can we determine the equation of a line perpendicular to FG that passes through H. Consequently, we cannot test which of the given points satisfies the condition.
Examples
In architecture, determining perpendicular lines is crucial for designing stable and aesthetically pleasing structures. If you're designing a building and need a wall perpendicular to another, you'd use the principles of coordinate geometry to ensure the lines are perfectly perpendicular, contributing to the building's structural integrity and visual harmony.
We cannot determine which point is on the perpendicular line to FG passing through point H because we do not have the coordinates of FG or H. Therefore, none of the given options can be evaluated as valid. Additional information is needed to solve the problem.
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