Question

Three points A, B, and C are collinear. A (1, -3) B (k, 3k) C (4, 3). What is the value of k if the slopes of AB and AC are equal.

Answer 1

To find the value of k if the slopes of AB and AC are equal, calculate the slopes of AB and AC and set them equal to each other. Solve the resulting equation to find the value of k.

Step-by-step explanation:

To find the value of k if the slopes of AB and AC are equal, we need to calculate the slopes of AB and AC and set them equal to each other.

The slope of a line is given by the formula: m = (y2 - y1) / (x2 - x1). Using the coordinates of points A and B, the slope of AB is: m(AB) = (3k - (-3)) / (k - 1).

Similarly, using the coordinates of points A and C, the slope of AC is: m(AC) = (3 - (-3)) / (4 - 1).

Setting the slopes of AB and AC equal to each other, we have: (3k - (-3)) / (k - 1) = (3 - (-3)) / (4 - 1).

Solving the equation will give us the value of k.