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Alex73 [517]
3 years ago
5

Given that OA = 2x + 9y, OB = 4x + 8y and CD = 4x - 2y, explain the geometrical relationships between the straight lines AB and

CD.
Mathematics
1 answer:
Step2247 [10]3 years ago
8 0

Answer:

The geometrical relationships between the straight lines AB and CD is that they have the same slope

Step-by-step explanation:

Given

OA = 2x + 9y

OB = 4x + 8y

CD = 4x - 2y

Required

The relationship between AB, CD

Since AB is a straight line and O is the origin, then:

AB = (c - a)x + (d - b)y

Where:

OA = ax + by ====> OA = 2x + 9y

OB = cx + dy ====> OB = 4x + 8y

This implies that:

a =2      b = 9     c = 4   d = 8  

So:

AB = (c - a)x + (d - b)y

AB = (4 - 2)x + (8 - 9)y

AB = 2x  -y

So, we have:

AB = 2x  -y

CD = 4x - 2y

Calculate the slope (m) of AB\ and\ CD

m = \frac{Coefficient\ of\ y}{Coefficient\ of\ y}

For AB

m_1 = \frac{-1}{2}

m_1 = -\frac{1}{2}

For CD

m_2 = \frac{-2}{4}

m_2 = \frac{-1}{2}

m_2 = -\frac{1}{2}

By comparison:

m_1 = m_2 = -\frac{1}{2}

This implies that both lines have the same slope

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