Question

Question 1Points W and X are on WX. Y and Z are on YZ. Are WX and YZ parallel, perpendicular, or neither? W(-2,4) X(1,1)Y(1,2) Z(5,-2)

Answer 1

Given:

The points W and X on the line WX are :

W(-2, 4), X(1, 1)

The points Y and Z on the line YZ are:

Y(1, 2), Z(5, -2)

We can check if the lines are parallel, perpendicular or neither by finding the slope/gradient of each line.

`\begin{gathered} \text{If m}_1=m_2\text{ (lines are parallel)} \\ \text{If m}_1\text{ =-}(1)/(m_2)\text{ (lines are perpendicular)} \end{gathered}`

The slope of any line can be found using the formula:

`\text{slope = }(y_2-y_1)/(x_2-x_1)`

The slope of line WX:

`\begin{gathered} \text{slope of WX = }(1-4)/(1-(-2)) \\ =\text{ }(-3)/(3) \\ =\text{ -1} \end{gathered}`

The slope of line YZ:

`\begin{gathered} \text{slope of YZ = }(-2-2)/(5-1) \\ =(-4)/(4) \\ =\text{ -1} \end{gathered}`

Since the slope of line WX is equal to the slope of line YZ, the lines are parallel.