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

Answer 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 = $\frac{-coefficient(x)}{coefficient(y)}$

∵ 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 = $\frac{-coefficient(x)}{coefficient(y)}$

∵ Coefficient of x = 2

∵ Coefficient of y = -1

∴ The slope of ab = $\frac{-2}{-1}=2$

∵ cd = 4 x - 2 y

∵ Coefficient of x = 4

∵ Coefficient of y = -2

∴ The slope of cd = $\frac{-4}{-2}=2$

∵ 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

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