Question #113959
determine whether the line through the pair of points A, B is
parallel or perpendicular to the line through the pair C, D.
3.) A(1,5), B(-7,1) and C(8,-2), D(4,6)
4.) A(6,2), B(8,6) and C(4,8), D(2,4)
1
Expert's answer
2020-05-05T20:13:46-0400

3) To find an angle, we should find slope k1k_1

for AB line and slope k2k_2 for CD line.

If we will choose equation of line AB as y=k1x+b1y=k_1\cdot x + b_1 so, we will have a system: {5=k11+b11=k1(7)+b1\begin{cases}5=k_1\cdot1+b_1 \\1=k_1\cdot(-7)+b_1\end{cases}From it, we could find that k1=0.5k_1=0.5

Like that, CD line has equation y=k2x+b2y=k_2\cdot x+b_2 and k2=2k_2=-2 .

As k1k2=1k_1\cdot k_2 = -1 it means that, these lines are perpendicular. The answer: AB and CD are perpendicular.



4) As the question above, we could find that k1=2, k2=2k_1=2,\space k_2=2 . As, k1=k2k_1 = k_2, AB and CD lines have equal slopes, more clearly, they are parallel lines. Answer: AB and CD lines are parallel


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