Answer to Question #113959 in Analytic Geometry for kath

Question

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)

Answer 1

3) To find an angle, we should find slope $k_1$

for AB line and slope $k_2$ for CD line.

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

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

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

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