Question

1. given a(-3, -2) b(9, 1), c(3, 6) and d(5, -2) determine if line ab and cd are parallel, perpendicular or neither (click here for video #7)

Explanation:

Step1: Calculate the slope of line AB

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For points \(A(-3,-2)\) and \(B(9,1)\), \(m_{AB}=\frac{1-(-2)}{9-(-3)}=\frac{1 + 2}{9+3}=\frac{3}{12}=\frac{1}{4}\)

Step2: Calculate the slope of line CD

For points \(C(3,6)\) and \(D(5,-2)\), \(m_{CD}=\frac{-2 - 6}{5 - 3}=\frac{-8}{2}=-4\)

Step3: Check the relationship between slopes

If two lines are parallel, \(m_1=m_2\). If two lines are perpendicular, \(m_1\times m_2=-1\).
Here, \(m_{AB}\times m_{CD}=\frac{1}{4}\times(-4)=-1\)

Answer:

Line \(AB\) and \(CD\) are perpendicular.