Answer:
x = 19/2
Step-by-step explanation:
The slopes of perpendicular lines have a product of -1.
Slope of line that passes through (4, 8) and (2, -1):
m1 = slope = (-1 - 8)/(2 - 4) = -9/(-2) = 9/2
Slope of perpendicular line is m2:
(m1)(m2) = -1
m2 = -1/m1 = -1/(9/2) = -2/9
The slope of the perpendicular line is -2/9
Now we write the expression for the slope of the second line. We use x for the unknown x-coordinate and -2/9 for the slope.
m2 = (5 - 2)/(-4 - x) = -2/9
3/(-4 - x) = -2/9
Cross multiply:
-2(-4 - x) = 3 * 9
8 + 2x = 27
2x = 19
x = 19/2
