Answer:
a. Not perpendicular.
b. Perpendicular.
Step-by-step explanation:
We need to check whether the segments through the origin and the points listed perpendicular.
Product of slopes of two perpendicular lines is -1.
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(a) The given points are (9,10) and (10,9).
Slope of line segment through (0,0) and (9,10) is
[tex]m_1=\dfrac{10-0}{9-0}=\dfrac{10}{9}[/tex]
Slope of line segment through (0,0) and (10,9) is
[tex]m_2=\dfrac{9-0}{10-0}=\dfrac{9}{10}[/tex]
Product of slopes is
[tex]m_1\cdot m_2=\dfrac{10}{9}\cdot \dfrac{9}{10}=1\neq -1[/tex]
Therefore, the line segments through the origin and the points (9,10) and (10,9) are not perpendicular.
(b) The given points are (9,6) and (4,-6).
Slope of line segment through (0,0) and (9,6) is
[tex]m_1=\dfrac{6-0}{9-0}=\dfrac{6}{9}=\dfrac{2}{3}[/tex]
Slope of line segment through (0,0) and (4,-6) is
[tex]m_2=\dfrac{-6-0}{4-0}=\dfrac{-6}{4}=-\dfrac{3}{2}[/tex]
Product of slopes is
[tex]m_1\cdot m_2=\dfrac{2}{3}\cdot (-\dfrac{3}{2})=-1[/tex]
Therefore, the line segments through the origin and the points (9,6) and (4,-6) are perpendicular.
