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.