Final answer:
To determine the value of k, we need to check if the three given points (A, B, and C) are collinear. Points are collinear if and only if the slope between any two points is the same. By finding the slope between A and B and setting it equal to the slope between A and C, we can solve for k. The value of k is approximately 11.98.
Step-by-step explanation:
To determine the value of k, we need to check if the three given points (A, B, and C) are collinear. Points are collinear if and only if the slope between any two points is the same. Since A(0, 6), B(3.6, 0), and C(k, -14) are collinear, the slope between A and B must be the same as the slope between A and C.
The slope between A and B can be found using the formula (y2 - y1) / (x2 - x1). So, the slope between A(0, 6) and B(3.6, 0) is (0 - 6) / (3.6 - 0) = -6 / 3.6 = -1.67.
To find the value of k, we can use the same slope formula between A(0, 6) and C(k, -14). Setting it equal to -1.67, we get (-14 - 6) / (k - 0) = -1.67. Solving this equation will give us the value of k.
-20 / k = -1.67
k = -20 / -1.67 = 11.98 (rounded to two decimal places)