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
Previous

lines are perpendicular to each other

Step-by-step 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 =

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

m = = = = 2

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

m = = = -

2 ≠ - , then lines are not parallel

2 × - = - 1 , then lines are perpendicular

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4