StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

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

Question

🧐 Not the exact question you are looking for?Go ask a question

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.

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.