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Given that OA = 2x + 9y, OB = 4x + 8y and CD = 4x - 2y, explain the

geometrical relationships between the straight lines AB and CD.

User Ringo
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Answer: The geometrical relationships between the straight lines ab and cd

is the straight line ab is parallel to the straight line cd

Explanation:

Let us revise some notes:

If a line is 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

To find the equation of AB subtract OB from OA, then AB = (c - a)x + (d - b)y

The slope of line AB =

∵ oa = 2 x + 9 y

∵ ob = 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

- Add like terms

∴ ab = (4 x - 2 x) + (8 y - 9 y)

∴ ab = 2 x + -y

∴ ab = 2 x - y

∵ The slope of ab =

∵ Coefficient of x = 2

∵ Coefficient of y = -1

∴ The slope of ab =

∵ cd = 4 x - 2 y

∵ Coefficient of x = 4

∵ Coefficient of y = -2

∴ The slope of cd =

∵ Parallel lines have same slopes

∵ Slope of ab = slope of cd

∴ ab // cd

The geometrical relationships between the straight lines ab and cd

is the straight line ab is parallel to the straight line cd

User Thomas Luechtefeld
by
8.0k points

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