Question

One line has a slope of -1/5, which of the following two points will give a line that is perpendicular to it?(0, 0) and (0, 5)(1, 4) and (2, 10)(1, 3) and (0, 8)(1, 3) and (2, 10)(1, 4) and (2, 9)

Answer 1

Two lines are perpendicular if and only if their slopes fullfil:

$m_1m_2=-1$

plugging the slope given we have:

$\begin{gathered} -\frac{1}{5}m_1=-1 \\ m_1=(-1)(-5) \\ m_1=5 \end{gathered}$

this means that the line we are looking for has slope 5.

Now, the slope of a line is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

we need to find two points that makes this slope equal to 5, choosing the points (1,4) and (2,9) we notice that:

$\begin{gathered} m=\frac{9-4}{2-1} \\ m=\frac{5}{1} \\ m=5 \end{gathered}$

Therefore the points we are looking for are (1,4) and (2,9)