Question

click and drag to plot a perpendicular line. the line will change colors when a parallel or perpendicular line is drawn accurately. answer original slope: blank perpendicular slope: blank

Explanation:

Step1: Select two points on the original line

Suppose two points on the original line are $(x_1,y_1)$ and $(x_2,y_2)$. From the graph, assume the original line passes through $(0, - 2)$ and $(2,2)$.

Step2: Calculate the original slope

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(0, - 2)$ and $(x_2,y_2)=(2,2)$ into it, we get $m=\frac{2-( - 2)}{2 - 0}=\frac{4}{2}=2$.

Step3: Calculate the perpendicular slope

If two lines are perpendicular, the product of their slopes is $-1$. Let the original slope be $m_1$ and the perpendicular slope be $m_2$, then $m_1m_2=-1$. Since $m_1 = 2$, then $m_2=-\frac{1}{2}$.

Answer:

Original Slope: $2$
Perpendicular Slope: $-\frac{1}{2}$