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?
Show Hint
When analyzing geometrical problems involving lines, make sure to verify all conditions, such as slope, intercepts, and distances, to spot inconsistencies.
The distance from the origin to one of the lines is \( \frac{3}{\sqrt{2}} \)
The distance between the x-intercepts of the two lines is 4
The distance between the y-intercepts of the two lines is 6
The line \( L_1 \) passes through the point (1, 0)
The distance from the origin to one of the lines is \( \frac{2}{\sqrt{5}} \)
Show Solution
The Correct Option isA
Solution and Explanation
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: \[\boxed{\text{(A) The distance from the origin to one of the lines is } \frac{3}{\sqrt{2}}}\]