Question

A straight line \( L_1 \) has the equation \( y = k(x - 1) \), where \( k \) is some real number. The straight line \( L_1 \) intersects another straight line \( L_2 \) at the point (5, 8). If \( L_2 \) has a slope of 1, which of the following is definitely FALSE?

• A. The distance from the origin to one of the lines is \( \frac{3}{\sqrt{2}} \)
• B. The distance between the x-intercepts of the two lines is 4
• C. The distance between the y-intercepts of the two lines is 6
• D. The line \( L_1 \) passes through the point (1, 0)
• E. The distance from the origin to one of the lines is \( \frac{2}{\sqrt{5}} \)

Hint:

When analyzing geometrical problems involving lines, make sure to verify all conditions, such as slope, intercepts, and distances, to spot inconsistencies.

Answer 1

The Correct Option is A

Step 1: Determine the equation for \( L_1 \).
The equation for line \( L_1 \) is provided as \( y = k(x - 1) \), with \( k \) representing the slope.
Step 2: Examine the provided choices.
Substituting the given slope and intersection point allows verification of the options. Option (A) is identified as the incorrect statement.
Final Answer: \[\boxed{\text{(A) The distance from the origin to one of the lines is } \frac{3}{\sqrt{2}}}\]