How do you determine if three points are collinear?

Answer 1

Since any 2 points determine 1 line, take 2 of the points and find the equation of the line drawn thru these 2 points.

Substitute the x and y of the either point into the equation and find the y-intercept (b)

Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are =.

(y2-y1) ÷ (x2 - x1) = slope

y = slope * x + b

Point # 1 = (6, 5)

Point # 2 = (10, 25)

Point # 3 = (12, 30)

Point # 4 = (12, 35)

(y2 - y1) ÷ (x2 - x1) = slope

(25 - 5) ÷ (10 - 6) = slope

(20) ÷ (4) = slope

Slope = 5

y = m * x + b

y = 5 * x + b

Substitute the x and y of the point (6, 5) into the equation and find the y-intercept (b)

y = 5 * x + b

5 = 5 * 6 + b

5 = 30 + b

b = -25

y = 5 * x - 25

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Check your points

Point # 1 = (6, 5)

5 = 5 * 6 - 25

5 = 30 - 25 OK

.

Point # 2 = (10, 25)

25 = 5 * 10 - 25

25 = 5 * 10 - 25 OK

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Then, substitute the x and y of the 3rd point into the equation and see if the both sides of the equation are

Point # 3 = (12, 30)

.

y = 5 * x - 25

30 = 5 * 12 - 25

30 = 60 - 25 = 35

Point # 3 = (12, 30) is not on the line

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Point # 4 = (12, 35)

35 = 5 * 12 - 25

35 = 60 - 25 =35

Point # 4 = (12, 35) is on the line