- Line k passes through (1, 1)
- Line m passes through (1, -1)
Target question: Are the lines k and m perpendicular to each other?
Note: two lines are said to be perpendicular if the product of their slope is -1
Statement 1 => lines k and m intersect a the point (1, -1), this means the second point of line k (1, -1)
$$Slope\ of\ k=\ \frac{dy}{dx}=\frac{y2-y1}{x2-x1}=\frac{-1-1}{1-1}=undefine$$
But the slope of m is unknown and we cannot determine if the two lines are perpendicular hence target question cannot be answered, therefore, statement 1 is NOT SUFFICIENT
Statement 2=> line k intersects the x-axis at the point (1, 0), this means the second point of line k = (1, 0)
$$Slope\ of\ k=\ \frac{dy}{dx}=\frac{y2-y1}{x2-x1}=\frac{0-1}{1-1}=undefine$$
But slope of m is unknown and we cannot determine if the two lines are perpendicular, hence, target question cannot be answered and statement 2 is NOT SUFFICIENT
Combining both statements together =>
Neither of the two statements gives any information about line m or its slope, So the target question still remains unanswered, hence, both statements together ARE NOT SUFFICIENT
Answer= E
