Answer:
- Lines m and n are not parallel;
- Lines m and p are not perpendicular;
- Lines n and p are perpendicular.
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We know parallel lines have equal slopes and perpendicular lines have opposite-reciprocal slopes.
Find the slope of each line using two points on the line.
Line m
- Points (0, 4) and (3, 6),
- slope (m) = (6 - 4)/(3 - 0) = 2/3.
Line n
- Points (0, -2) and (5, 1),
- slope (n) = (1 - (-2))/(5 - 0) = 3/5.
Line p
- Points (-3, 6) and (0, 1),
- slope (p) = (1 - 6)/(0 - (-3)) = - 5/3.
Compare the slopes of m and n:
- 2/3 ≠ 3/5, lines m and n are not parallel.
The product of slopes of m and p should be - 1 if perpendicular:
- 2/3 × - 5/3 = - 10/9 ≠ - 1, these lines are not perpendicular
The product of slopes of n and p should be - 1 if perpendicular:
- 3/5 × (- 5/3) = - 1, these lines are perpendicular