Determine which of the lines, I any, are parallel or perpendicular. Explain.
1 answer:
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Answer:
1. line b is perpendicular to the other two, which are parallel
2. line a is perpendicular to the other two, which are parallel
Step-by-step explanation:
1. The differences between coordinates (∆x, ∆y) are ...
(-2, 3) -(1, -1) = (-3, 4) . . . line a
(-3, 1) -(1, 4) = (-4, -3) . . . line b
(0, 2) -(3, -2) = (-3, 4) . . . line c
When the (∆x, ∆y) values are identical, the lines are parallel. If the values are swapped, and one differs in sign, the lines are perpendicular.
line b is perpendicular to lines a and b, which are parallel
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2. When all of the equations are written in standard form, they are ...
- 4x +y = 7 . . . line a
- x -4y = 2 . . . line b
- x -4y = 3 . . . line c
As above, when the x- and y-coefficients are identical, the lines are parallel. If they are swapped and one is negated, the lines are perpendicular.
line a is perpendicular to lines b and c, which are parallel
__
In the attached graph, the lines of part 1 are blue; those of part 2 are red.
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