Question

question 4 score: 0 of 1 point one line goes through the points (3,2) and (−4,5). another line passes through (4,5) and (−3,2). determine if these two lines are parallel, perpendicular, or neither. a parallel b perpendicular c neither current learning objective: determining whether graphs of lines are parallel or perpendicular category: quiz (11) ** test 1 a(chapters 2 and 15) math 1111 - 08 assignments > test 1 a(ch... welcome to mathgpt! to get started, simply click the ask mathgpt button under the question. well be here with you each step of the way! mathgpt may provide inaccurate information, please verify its responses. terms privacy ask mathgpt

Explanation:

Step1: Calculate slope of first line

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the points $(3,2)$ and $(-4,5)$, we have $m_1=\frac{5 - 2}{-4 - 3}=\frac{3}{-7}=-\frac{3}{7}$.

Step2: Calculate slope of second line

For the points $(4,5)$ and $(-3,2)$, using the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_2=\frac{2 - 5}{-3 - 4}=\frac{-3}{-7}=\frac{3}{7}$.

Step3: Check relationship between slopes

Two lines are parallel if $m_1 = m_2$, perpendicular if $m_1\times m_2=-1$, and neither if neither of these conditions are met. Here, $m_1
eq m_2$ and $m_1\times m_2=(-\frac{3}{7})\times\frac{3}{7}=-\frac{9}{49}
eq - 1$.

Answer:

C. neither