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