Classify parallel and perpendicular lines EXAMPLE 4 Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (– 2, 2) and (0, –

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Presentation transcript:

Classify parallel and perpendicular lines EXAMPLE 4 Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (– 2, 2) and (0, – 1) a. Line 2: through (– 4, – 1) and (2, 3) Line 1: through (1, 2) and (4, – 3) b. Line 2: through (– 4, 3) and (– 1, – 2) SOLUTION Find the slopes of the two lines. a.a. m 1 = –1 – 2 0 – (– 2) = – 3 2 = 3 2 –

Classify parallel and perpendicular lines EXAMPLE 4 m 2 = 3 – (– 1) 2 – (– 4) = 4 6 = 2 3 ANSWER Because m 1 m 2 = – = – 1, m 1 and m 2 are negative reciprocals of each other. So, the lines are perpendicular.

Classify parallel and perpendicular lines EXAMPLE 4 Find the slopes of the two lines. b.b. m 1 = –3 – 2 4 – 1 = – 5 3 = 5 3 – m 2 = – 2 – 3 – 1 – (– 4) = – 5 3 = 5 3 – ANSWER Because m 1 = m 2 (and the lines are different), you can conclude that the lines are parallel.

GUIDED PRACTICE for Example 4 GUIDED PRACTICE Tell whether the lines are parallel, perpendicular, or neither. 11. Line 1 : through (– 2, 8) and (2, – 4) Line 2 : through (– 5, 1) and (– 2, 2) SOLUTION Find the slopes of the two lines. a.a. m 1 = –4 – 8 2 – (– 2) = – 3 m 2 = 2 – 1 – 2 – (– 5) = 1 3

GUIDED PRACTICE for Example 4 GUIDED PRACTICE ANSWER Because m 1 m 2 = – = – 1, m 1 and m 2 are negative reciprocals of each other. So, the lines are perpendicular.

GUIDED PRACTICE for Example 4 GUIDED PRACTICE 12. Line 1 : through (– 4, – 2) and (1, 7) Line 2 : through (– 1, – 4) and (3, 5) SOLUTION Find the slopes of the two lines. a.a. m 1 = 7 – (– 2) 1 – (– 4) = m 2 = 5 – (– 4) 3 – (– 1) =

GUIDED PRACTICE for Example 4 GUIDED PRACTICE ANSWER Because m 1 = m 2 and m 1 and m 2 are not reciprocals of each other. So, the lines are neither

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