Question

Line A passes through the points (0,2) and (2,−2). Line B passes through the points (0,4) and (1,2). Line C passes through the points (0,−1) and (4,1). Identify which lines are parallel and which lines are perpendicular.

Answer 1

Answer:

A || B, A ⊥ C, B ⊥ C

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\m_1,\ m_2-\ slope\\b_1,\ b_2-\ y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\-----------------------$

$\text{We have points through which the line passes}\\\\Line\ A:\ (0,\ 2),\ (2,\ -2).\\Line\ B:\ (0,\ 4),\ (1,\ 2).\\Line\ C:\ (0,\ -1),\ (4,\ 1).\\\\\text{Calculte the slopes:}$

$m_A=\dfrac{-2-2}{2-0}=\dfrac{-4}{2}=-2\\\\m_B=\dfrac{2-4}{1-0}=\dfrac{-2}{1}=-2\\\\m_C=\dfrac{1-(-1)}{4-0}=\dfrac{2}{4}=\dfrac{1}{2}\\\\m_A=m_B\to\text{therefore the lines A and B are parallel}\\\\\begin{array}{ccc}m_Am_C=-2\cdot\dfrac{1}{2}=-1\\\\m_Bm_C=-2\cdot\dfrac{1}{2}=-1\end{array}\to\begin{array}{ccc}\text{therefore the lines A and C}\\\text{and B and C are perpendicular}\end{array}$