Question

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:(3,6),(-1,-5) )

( l_2:(-2,3),(4,7) )

Explanation:

Step1: Calculate the slope of \(L_1\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For \(L_1\) with \((x_1,y_1)=(3,6)\) and \((x_2,y_2)=(-1,-5)\),
\(m_1=\frac{-5 - 6}{-1 - 3}=\frac{-11}{-4}=\frac{11}{4}\)

Step2: Calculate the slope of \(L_2\)

For \(L_2\) with \((x_1,y_1)=(-2,3)\) and \((x_2,y_2)=(4,7)\),
\(m_2=\frac{7 - 3}{4 - (-2)}=\frac{4}{6}=\frac{2}{3}\)

Step3: Check the relationship between slopes

Since \(m_1
eq m_2\) (so not parallel) and \(m_1\times m_2=\frac{11}{4}\times\frac{2}{3}=\frac{11}{6}
eq - 1\) (so not perpendicular)

Answer:

neither