## given that oa=2x+9y ob=4x+8y and cd= 4x-2y, explain the geometrical relationships between the straight lines ab and cd mathswatch answer

Question

given that oa=2x+9y ob=4x+8y and cd= 4x-2y, explain the geometrical relationships between the straight lines ab and cd mathswatch answer

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2 weeks 2021-10-13T23:29:00+00:00 1 Answer 0

1. The geometrical relationships between the straight lines ab and cd

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

Step-by-step 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

∴ 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