Answer:
The geometrical relationships between the straight lines AB and CD is that they have the same slope
Step-by-step explanation:
Given
[tex]OA = 2x + 9y[/tex]
[tex]OB = 4x + 8y[/tex]
[tex]CD = 4x - 2y[/tex]
Required
The relationship between AB, CD
Since AB is a straight line and O is the origin, then:
[tex]AB = (c - a)x + (d - b)y[/tex]
Where:
[tex]OA = ax + by[/tex] ====> [tex]OA = 2x + 9y[/tex]
[tex]OB = cx + dy[/tex] ====> [tex]OB = 4x + 8y[/tex]
This implies that:
[tex]a =2[/tex] [tex]b = 9[/tex] [tex]c = 4[/tex] [tex]d = 8[/tex]
So:
[tex]AB = (c - a)x + (d - b)y[/tex]
[tex]AB = (4 - 2)x + (8 - 9)y[/tex]
[tex]AB = 2x -y[/tex]
So, we have:
[tex]AB = 2x -y[/tex]
[tex]CD = 4x - 2y[/tex]
Calculate the slope (m) of [tex]AB\ and\ CD[/tex]
[tex]m = \frac{Coefficient\ of\ y}{Coefficient\ of\ y}[/tex]
For AB
[tex]m_1 = \frac{-1}{2}[/tex]
[tex]m_1 = -\frac{1}{2}[/tex]
For CD
[tex]m_2 = \frac{-2}{4}[/tex]
[tex]m_2 = \frac{-1}{2}[/tex]
[tex]m_2 = -\frac{1}{2}[/tex]
By comparison:
[tex]m_1 = m_2 = -\frac{1}{2}[/tex]
This implies that both lines have the same slope
