Line with slope greater than 1 passes A(4, 3) and intersects x–y=2 at B

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

1. 2x + y = 9
2. 3x – 2y = 7
3. x + 2y = 6
4. 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