Question

is ab parallel to cd? explain. no, because the slopes of the lines are not equal. no, because the slopes of the lines are not opposite reciprocals of each other. yes, because both lines have a slope of -4/3. yes, because both lines have a slope of -3/4.

Explanation:

Step1: Recall slope - formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate slope of \(\overrightarrow{AB}\)

For points \(A(-3,3)\) and \(B(0,1)\), \(m_{AB}=\frac{1 - 3}{0+3}=\frac{-2}{3}=-\frac{2}{3}\).

Step3: Calculate slope of \(\overrightarrow{CD}\)

For points \(C(0, - 5)\) and \(D(3,-1)\), \(m_{CD}=\frac{-1 + 5}{3-0}=\frac{4}{3}\).

Step4: Check parallel - condition

Parallel lines have equal slopes. Since \(m_{AB}
eq m_{CD}\), the lines are not parallel.

Answer:

No, because the slopes of the lines are not equal.