Problema Solution
Line m contains the points, A(–2, 6) and B(4, 8), while line n contains the C(8, 12) and D(x, 24).
1. Given m and n are perpendicular lines, solve for the value of x.
2. Given m and n are parallel lines, solve for the value of x.
In your final answer, include all formulas and calculations necessary to solve for x.
Answer provided by our tutors
The equation of the line is:
y = mx + b, where "m" is the slope and "b" gives the y-intercept
m = (y2 - y1)/(x2 - x1)
In our case for line m we have: x1 = -2, y1 = 6, x2 = 4, y2 = 8
m1 = (8 - 6)/(4 - (-2))
m1 = 2/6
m1 = 1/3
For line n we have: x1 = 8, y1 = 12, x2 = x, y2 = 24
m2 = (24 - 12)/(x - 8)
m2 = 12/(x - 8)
1. Given m and n are perpendicular lines, solve for the value of x.
Lines m and n are perpendicular if and only if m1*m2 = -1 that is:
(1/3)*12/(x - 8) = -1
........
........
x = 4
2. Given m and n are parallel lines, solve for the value of x.
Lines m and n are perpendicular if and only if m1=m2 that is:
1/3 = 12/(x - 8)
........
........
x = 44