Respuesta :
The streets are neither perpendicular nor parallel
Here, we want to determine if the streets are parallel
To get this, we will need to get the slope of the two roads
If the streets are parallel, their slope will be equal. However, if the streets are perpendicular, the product of their slopes will be equal to -1
Let us proceed to find the slopes of both streets
Mathematically, we can use the equation below to find the slopes of the streets;
[tex]\begin{gathered} \text{For Elmwood Drive;} \\ m_{1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m_{1\text{ }}=\frac{-9-(-11)}{0-4}=\frac{2}{-4}=-\frac{1}{2}\text{ } \\ \\ \text{For Taylor Road;} \\ \\ m_2\text{ = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{-5-(-2)}{4-6}\text{ = }\frac{-3}{-2}\text{ = }\frac{3}{2} \end{gathered}[/tex]From the slopes calculated, we can see that the streets are neither perpendicular nor parallel. This is because the products of their slopes is neither equal to -1 nor the slopes are equal
