Question

Given that OA = 3x + 7y, OB = 5x + 6y and CD = 6x – 3y, explain the

geometrical relationships between the straight lines AB and CD.

Answer 1

Parallel to each other + CD is 3 times longer

Explanation:

They are parallel

5x + 6y - (3x + 7y)

= 2x - y

6x - 3y = 3 (2x -y)

Both 2x -y one of them is just 'three times' so they are PARALLEL TO EACH OTHER and CD is 3 times longer.

Answer 2

CD is 3 times as long as AB

Explanation:

You want to know the relationship between AB and CD, given OA=3x+7y, OB=5x+6y, and CD=6x-3y.

Line AB

The length of line AB is the difference in the coordinates of its end points:

AB = B -A = (5x +6y) -(3x +7y) = (5 -3)x +(6 -7)y

AB = 2x -y

Line CD

The length of line CD can be written as a product:

CD = 6x -3y = 3(2x -y)

Substituting for 2x-y, we have ...

CD = 3·AB

The line CD is 3 times the length of the line AB.

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