Question

15 fill in the blank 1 point
determine whether the lines ( l_1 ) and ( l_2 ) that pass through the pairs of points are parallel, perpendicular or neither. (note: type your answer in small letters).
( l_1: (-1,2), (-1,4) )
( l_2: (7,3), (4,7) )
type your answer...

Explanation:

Step1: Calculate the slope of \(L_1\)

For a line passing through \((x_1,y_1)\) and \((x_2,y_2)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For \(L_1\) with \((x_1=-1,y_1 = 2)\) and \((x_2=-1,y_2 = 4)\), \(m_1=\frac{4 - 2}{-1-(-1)}=\frac{2}{0}\), which means \(L_1\) is a vertical line (\(x=-1\)).

Step2: Calculate the slope of \(L_2\)

For \(L_2\) with \((x_1 = 7,y_1=3)\) and \((x_2 = 4,y_2 = 7)\), \(m_2=\frac{7 - 3}{4 - 7}=\frac{4}{-3}=-\frac{4}{3}\). A vertical line (undefined slope) and a non - horizontal line (slope \(m =-\frac{4}{3}\)) are perpendicular.

Answer:

perpendicular