Question

Are the segments through the origin and the points listed perpendicular? Explain.

Answer 1

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.

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

(a) The given points are (9,10) and (10,9).

Slope of line segment through (0,0) and (9,10) is

$m_1=\dfrac{10-0}{9-0}=\dfrac{10}{9}$

Slope of line segment through (0,0) and (10,9) is

$m_2=\dfrac{9-0}{10-0}=\dfrac{9}{10}$

Product of slopes is

$m_1\cdot m_2=\dfrac{10}{9}\cdot \dfrac{9}{10}=1\neq -1$

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

$m_1=\dfrac{6-0}{9-0}=\dfrac{6}{9}=\dfrac{2}{3}$

Slope of line segment through (0,0) and (4,-6) is

$m_2=\dfrac{-6-0}{4-0}=\dfrac{-6}{4}=-\dfrac{3}{2}$

Product of slopes is

$m_1\cdot m_2=\dfrac{2}{3}\cdot (-\dfrac{3}{2})=-1$

Therefore, the line segments through the origin and the points  (9,6) and (4,-6) are perpendicular.