Question

Answer fast plz

Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (–2, 1), (3, 11)
Line 2: (0,4), (2,3)
parallel
Operpendicular
neither
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Answer 1

lines are perpendicular to each other

Explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines = - 1

Calculate the slopes of the lines using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (3, 11 )

m =
`(11-1)/(3-(-2))` =
`(10)/(3+2)` =
`(10)/(5)` = 2

Repeat with (x₁, y₁ ) = (0, 4 ) and (x₂, y₂ ) = (2, 3 )

m =
`(3-4)/(2-0)` =
`(-1)/(2)` = -
`(1)/(2)`

2 ≠ -
`(1)/(2)` , then lines are not parallel

2 × -
`(1)/(2)` = - 1 , then lines are perpendicular