Question

Given that OA = 2x + 9y , OB = 4x + 8y and CD = 4x - 2y , explain the geometrical relationships between the straight line AB and CD.
It’s a 3 mark question sooo if someone could help then thanks.

Answer 1

The geometrical relationships between the straight lines AB and CD is that they are parallel to each other

How to determine the relationship

It is important to note the following;

• A drawn from the origin and passes through point A (a , b), then the equation of OA = ax + by

• If a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy

We  find the equation of AB by subtracting OB from OA, thus AB = (c - a)x + (d - b)y

The slope of line AB =

⇒ OA= 2 x + 9 y

⇒ OA = 4 x + 8 y

⇒AB = OB - OA

⇒AB = (4 x + 8 y) - (2 x + 9 y)

⇒ AB = 4 x + 8 y - 2 x - 9 y

Collect like terms

⇒ AB = (4 x - 2 x) + (8 y - 9 y)

⇒AB = 2 x + -y

⇒ AB = 2 x - y

⇒ Coefficient of x = 2

⇒ Coefficient of y = -1

⇒ The slope of ab = $\frac{-2}{-1}$ = 2

For CD

⇒ CD = 4 x - 2 y

⇒Coefficient of x = -4

⇒ Coefficient of y = -2

⇒The slope of cd = $\frac{-4}{-2}$ = 2

Note that Parallel lines have same slopes

And Slope of ab = slope of cd

AB // CD

Therefore, the geometrical relationships between the straight lines AB and CD is that they are parallel to each other

Learn more about parallel lines here:

brainly.com/question/24607467

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