Question

Determine which of the lines, I any, are parallel or perpendicular. Explain.

1. Line a passes through (-2, 3) and (1. -1). 2. Line & y = --4x + 7
Line b passes through (-3, 1) and (1. 4). Line b: x = 4y + 2
Line c passes through (0, 2) and (3, -2). Linee - 4y + r = 3
HELP PLEASE

Answer 1

9514 1404 393

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

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

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In the attached graph, the lines of part 1 are blue; those of part 2 are red.