Question

question
find the slope of segments $overline{ab}$ and $overline{xy}$. are the lines parallel, perpendicular, or neither?
$a(3,4)$, $b(2, - 3)$
$x(1,-2)$, $y(0,5)$
answer attempt 1 out of 2
slope of ab =
slope of xy =

Explanation:

Step1: Recall slope formula

The slope formula between 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 AB

For points $A(3,4)$ and $B(2,-3)$, we have $x_1 = 3,y_1=4,x_2 = 2,y_2=-3$. Then $m_{AB}=\frac{-3 - 4}{2 - 3}=\frac{-7}{-1}=7$.

Step3: Calculate slope of XY

For points $X(1,-2)$ and $Y(0,5)$, we have $x_1 = 1,y_1=-2,x_2 = 0,y_2=5$. Then $m_{XY}=\frac{5-(-2)}{0 - 1}=\frac{7}{-1}=-7$.

Step4: Determine relationship

Since $m_{AB}=7$ and $m_{XY}=-7$, $m_{AB}
eq m_{XY}$ (not parallel) and $m_{AB}\times m_{XY}=7\times(-7)= - 49
eq - 1$ (not perpendicular). So they are neither parallel nor perpendicular.

Answer:

Slope of AB = 7
Slope of XY = -7
Neither