Determine which lines, if any, are parallel or perpendicular. Explain. Line a passes through (0,4) and (4,3).
Line b passes through (0, 1) and (4,0).
Line c passes through (2,0) and (4,4).
are parallel, because they have
Ja are perpendicular, because they
have slopes that are

Help!!!

line a and b are parallel, there is no perpendicular lines

Step-by-step explanation:

Looking at the slope of each line, you can identify whether the lines are parallel, perpendicularlar, or neither.

When the slopes are the same, they are parallel.

When the slopes have opposite sign and numerator and denominator flipped, they are perpendicular. Ex. and are perpendicular slopes.

Finding slope is using the formula:

Line a has slope   =

Line b also has slope

Line c has slope 2

Since slope of line a and b are same, they are parallel.

Line c is not perpendicular to line a and b because the slope should have opposite sign and numerator and denominator flipped, which is 4 not 2.

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