Determine whether the three points are collinear. See Example 4. ...

Question

Determine whether the three points are collinear. See Example 4. (0,-7),(-3,5),(2,-15)

Accepted Answer

Identiod if they're given set of points are co linear and were given a set of three points now determine that points are killed in here. We'll see the distance between our points If the sum of our two shortest distances, it's the same thing as our longest distance. We can go ahead and say that they are co linear. Let's go and find the distance between all these points. Let's take the of point A and B. First. Or in other words, our first two points distance formula. See him by the square root of X two minus X one squared plus Y two minus Y one squared. So then we can use the distance of our points here. Our first point A And our 2nd Point B will use 89889264. You wanna x two first. So we'll say negative six is first minus negative eight for other X plus 4 -8 Squared there. Simplify this. We will get square root four Plus 16 which gives a square of 20 Which you can find simplify as two squares of five. Let's check our other points. Let's take a B C. Next or our second point in our third point, if you look here, we want negative 64 negative two negative four negative two minus negative six squared plus -4 -4 Squared risk is us square root 16 Plus the square of 64 of which goes to four squares of five fine. Let's check a C. So our first point in the third point negative two minus negative eight squared Plus the 4 -8 squeaked which goes to the square 36 plus 1 44 square of 1 80. Which then simplifies as a square five times 6. So we write 6 4-5 like so I want to see if the some of the shortest distances are equal to our longest distance. So our shortest distances are two squares of five and four squares of five. Now is this equal to six square to five? Which is the longest distance? We will then say yes. It is there the same number if you add them together? Because this is the same number, we can say that given set of points are indeed ca linear, which means we have answer a Yes. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

Determine whether the three points are collinear. See Example 4. (0,-7),(-3,5),(2,-15)

Key Concepts

Collinearity of Points

Slope Calculation

Determinants in Geometry

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