A line with a slope greater than 1 passes through point A(4, 3) and intersects the line x – y – 2 = 0 at point B. If the length of the line segment AB is , then B also lies on the line

- 2x + y = 9
- 3x – 2y = 7
- x + 2y = 6
- 2x – 3y = 3

## Solution:

Firstly make the graph according to the question.

Use the formula to find the length of the line segment.

Then identify which line satisfy point B.

### Step 1 of 3:

According to the question, we get

### Step 2 of 3:

We have A(4, 3)

Let B(a, b) = B(a, a-2)

Also, given that length of line segment AB =

But we know that,

If then length

On squaring both sides

Now, On the factorisation of the quadratic equation, we get

or

When

When

or

### Step 3 of 3:

Line x + 2y = 6 is satisfy by

## Final Answer:

Hence, Option (C) is correct

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