You are watching: Do the points lie on the same line

Click right here to see ALL troubles on Length-and-distanceQuestion 530663: show that the 3 points (-3,4) (3,2) (6,1) lie in the same line answer by oberobic(2304) (Show Source): You deserve to put this equipment on your website! The 3 points are: (-3,4) (3,2) (6,1)..Use the an initial two point out to specify the slope of the line.Then usage the third point to specify "b" such that the heat goes with the third point..m = (4-2) / (-3-3) = 2/-6 = -1/3.y = -1/3x + b.Use the 3rd point (6,1) to specify "b".1 = (-1/3)(6) + b1 = -2 + bb = 3.y = -1/3x +3..Of course, the next question that could be inquiry is whether the defined line is the just line that contains all 3 points..Recall the 3 points are: (-3,4) (3,2) (6,1). This time let"s usage (3,2) (6,1) to specify the line and (-3,4) to uncover "b"..m = (2-1)/(3-6) = 1/-3 = -1/3..We know immediately that with the exact same slope, the lines room parallel.Given they"re parallel and that lock go v the same points, then they have to lie on top of one another. Visually, they room the very same line. But we can continue this example, to discover the full equation..y = -1/3*x + b.Use (-3,4) to uncover b..4 = -1/3*-3 + b4 = 1 + bb = 3.y = -1/3*x + 3, i m sorry is the very same equation as discovered above..Remember, this inquiry asked if the 3 specific points lie on the same line. Lock do. .However, you have to realize any type of 3 points may

**not**to the right on the exact same line. There is no general law that any 3 points heat on a straight line. .Consider the points: (0,0), (1,1), and also (0,1). They carry out not lied on the same line.The points (0,0) and (1,1) heat on the acquainted line y=x, which has a slope = 1.The line connecting (0,0) and also (0,1) is a vertical line that has actually an unknown slope and does no go v (1,1). The heat connecting (0,1) and (1,1) is a horizontal line v slope = 0 and does no go v (0,0)..Our intuition may be the if 3 currently lie on the same line, there is only one equation the fits the line to the 3 points.

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But I leaving it to you come prove or disprove the intuition.