2. Let u be a directed line segment from P = (0,0) to Q = (3, 2) and v be a directed line segment from R= (1, 2) to S = (4,4). Which of the following is true?
(A) u is greater than ||v||
(B) ||u|| is less than || ||
(C) u = y
(D) uv

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step-by-step explanation:

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

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step-by-step explanation:

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