Answer:
a. x +2y -1 = 0
b. x -y = 3
Step-by-step explanation:
A line perpendicular to a given line will have a slope that is the opposite reciprocal of the slope of the given line. Using any equation of a line as a starting point, the equation of the perpendicular line can be written by interchanging the coefficients of x and y, and negating one of them.
The constant (c) in the equation will need to be chosen to make the line go through some particular point. This is generally accomplished by substituting the (x, y) values into the equation and choosing the constant to make it true.
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a.
2x -y -1 = 0 . . . . . given line
x +2y -c = 0 . . . . . perpendicular line
x +2y -(2 +2(-1/2)) = 0 . . . . . . through the point (x, y) = (2, -1/2)
x +2y -1 = 0
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b.
2x +2y = 5 . . . . . given line
x -y = c . . . . . . . . perpendicular line (common factor of 2 divided out)
x -y = 1 -(-2) . . . . . . . . through the point (x, y) = (1, -2)
x -y = 3
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Additional comment
The attachment shows the original lines as dashed, and the perpendicular lines as solid. The required points are also identified.
