Find the value of k, if the points (10, 14), (–3, 3) and (k, –8) are collinear ?

To find the value of k, we need to use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). Since the points are collinear, the slopes of the line segments between the points should be equal.

First, let's find the slope between the points (10, 14) and (-3, 3):

Slope = (3 - 14) / (-3 - 10) = -11 / -13 = 11/13

Next, let's find the slope between the points (10, 14) and (k, -8):

Slope = (-8 - 14) / (k - 10) = -22 / (k - 10)

Since the points are collinear, these two slopes should be equal:

11/13 = -22 / (k - 10)

Solving this equation for k gives:

k - 10 = -22 * 13 / 11

k - 10 = -26

k = -26 + 10

k = -16

So, the value of k that makes the points collinear is -16.