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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
- 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
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