Question

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

a. ????(9,10), ????(10,9)
b. ????(9,6), ????(4, −6)

Answer 1

b

Explanation:

Answer 2

a. Not perpendicular.

b. Perpendicular.

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=(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=(10-0)/(9-0)=(10)/(9)`

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

`m_2=(9-0)/(10-0)=(9)/(10)`

Product of slopes is

`m_1\cdot m_2=(10)/(9)\cdot (9)/(10)=1\\eq -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=(6-0)/(9-0)=(6)/(9)=(2)/(3)`

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

`m_2=(-6-0)/(4-0)=(-6)/(4)=-(3)/(2)`

Product of slopes is

`m_1\cdot m_2=(2)/(3)\cdot (-(3)/(2))=-1`

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