Final answer:
To find the value of x, we can determine the equation of the line passing through the given points and use the negative reciprocal of its slope to find the slope of the perpendicular line. By substituting the known point and slope into the point-slope form, we can solve for x.
Step-by-step explanation:
To find the value of x, we need to determine the equation of the line passing through the points (8, 12) and (x, 24). Since the line perpendicular to it passes through the points (-2, 6) and (4, 8), we can calculate the slope of the second line by taking the negative reciprocal of the slope of the first line.
Slope of the first line: m1 = (8 - 12) / (8 - x) = 4 / (8 - x)
Slope of the second line: m2 = -1 / m1 = -1 / (4 / (8 - x)) = -(8 - x) / 4
Since the second line passes through the point (4, 8), we can use the point-slope form of a line to obtain:
y - 8 = -(8 - x) / 4 * (x - 4)
Simplifying and solving for x will give us the value:
x = 2