Final answer:
The statement that 'All three are mutually perpendicular to each other' is not true for triangle ABC with the given vertices, as the slopes of the line segments do not produce a product of -1.
Step-by-step explanation:
When analyzing the vertices of triangle ABC with vertices A(0, -1), B(6, 5), and C(-4, 3), we must consider if the statement "All three are mutually perpendicular to each other" holds true. To determine this, we need to calculate the slopes of the line segments AB, BC, and AC. If two lines are perpendicular, the product of their slopes is -1.
The slope of AB is calculated by (5 - (-1)) / (6 - 0) = 6 / 6 = 1. The slope of BC is (3 - 5) / (-4 - 6) = -2 / -10 = 1/5. Last, the slope of AC is (3 - (-1)) / (-4 - 0) = 4 / -4 = -1.
Examining the slopes, none of the products of the slopes of any two line segments equal -1. Therefore, the lines AB, BC, and AC are not mutually perpendicular. Statement b is not true. Furthermore, the statement a is also incorrect as the line segments are not along the x-axis nor parallel to each other. Since none of the given statements a or b is true, it's possible the question is missing the correct statement or the options provided are not sufficient to describe triangle ABC.