Question

line a passes through points (13, 29) and (57, 78). line b passes through points (6, 72) and (55, 28). are line a and line b parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line a

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line a with points $(13,29)$ and $(57,78)$, $m_a=\frac{78 - 29}{57 - 13}=\frac{49}{44}$.

Step2: Calculate slope of line b

For line b with points $(6,72)$ and $(55,28)$, $m_b=\frac{28 - 72}{55 - 6}=\frac{-44}{49}$.

Step3: Check relationship

Two lines are parallel if $m_1 = m_2$ and perpendicular if $m_1\times m_2=- 1$. Here, $m_a\times m_b=\frac{49}{44}\times\frac{-44}{49}=-1$.

Answer:

perpendicular