Question

Are these lines perpendicular?While these lines mayappear to intersect at a 90°angle, it is best to find theirslopes to make sure.Orange lineriseSlope =runBlue line[?]runHint: Now enter the rise, or change in y-value, of the blue line.Remember, if the line is decreasing, your value should be negative.=WINSlope = rise=

Answer 1

The lines are not perpendicular

Step-by-step explanation:

We are to calculate the slope from the information given to us and to determine if the lines are perpendicular. This is shown below:

Orange line

`\begin{gathered} slope,m=(rise)/(run)=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ slope,m=(y_2-y_1)/(x_2-x_1) \\ \text{From the ordered pair that lie along the orange line, we have:} \\ (x_1,y_1)=(0,0) \\ (x_2,y_2)=(3,2) \\ \text{Substitute these into the formula, we have:} \\ slope,m=(2-0)/(3-0) \\ slope,m=(2)/(3) \end{gathered}`

Blue line

`\begin{gathered} slope,m=(rise)/(run)=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ slope,m=(y_2-y_1)/(x_2-x_1) \\ \text{From the ordered pair that lie along the blue line, we have:} \\ (x_1,y_1)=(0,0) \\ (x_2,y_2)=(-1,2) \\ \text{Substitute these into the formula, we have:} \\ slope,m=(2-0)/(-1-0) \\ slope,m=(2)/(-1)=-(2)/(1) \\ slope,m=-(2)/(1) \end{gathered}`

For perpendicular lines, the relationship between their slope is that they are negative reciprocals of each other. This is given by the formula:

`\begin{gathered} m=-(1)/(m_(perpendicular)) \\ \text{If the orange and blue lines are perpendicular, then this should be true:} \\ m_(orange)=-(1)/(m_(blue)) \\ (2)/(3)=(-1)/(-2) \\ (2)/(3)=(1)/(2)(FALSE) \\ (2)/(3)\\e(1)/(2) \\ \\ \therefore(2)/(3)\\e(1)/(2) \end{gathered}`

Therefore, the lines are not perpendicular