Answer:
Perpendicular
Explanation:
Find the slope for the points (5, 10) and (1, 6)
[tex]x_1=5,\text{ y}_1=10,\text{ x}_2=1,\text{ y}_2=6[/tex]
The slope is calculated below
[tex]\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ \\ m_1=\frac{6-10}{1-5} \\ \\ m_1=\frac{-4}{-4} \\ \\ m_1=1 \end{gathered}[/tex]
For the points (2,-6) and (-1, -3)
[tex]\begin{gathered} m_2=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m_2=\frac{-3-(-6)}{-1-2} \\ \\ m_2=\frac{-3+6}{-3} \\ \\ m_2=\frac{3}{-3} \\ \\ m_2=-1 \end{gathered}[/tex]
Note that:
[tex]\begin{gathered} m_1m_2=1(-1) \\ \\ m_1m_2=-1 \end{gathered}[/tex]
Since the product of the two slopes is -1, the lines through the pairs of points are perpendicular
