Question

Consider the four points used in Problem 1: (-9,13), (-3, 9), (3, 6) and (9, 1) Three out of four of these points lie on one line. Which one of the four points does not lie on the same line as the other three? Justify your answer using slope. b) Find the equation of the line that contains three out of the four points

Answer 1

Answer:

a) ( 3 , 6 )

b) y = -2*x / 3 + 7

Step-by-step explanation:

Given:

- The four points are:

                        (-9,13), (-3, 9), (3, 6) and (9, 1)

- Three points lie on the same line.

Find:

Which one of the four points does not lie on the same line as the other three?

Solution:

- Compute the slope between each pair of point:

                                 (-9,13), (-3, 9)

                        m_1 = ( 9 - 13 ) / ( -3 + 9 ) = - 2/3

                                 (-9,13), (3, 6)

                        m_2 = ( 6 - 13 ) / ( 3 + 9 ) = - 0.5833

                                 (-9,13), (9, 1)

                        m_3 = ( 1 - 13 ) / ( 9 + 9 ) = - 2/3

- We see that m_1 = m_3 ≠ m_2 . Hence, point ( 3 ,6 ) does not lie on the same line.

- The equation of line is expressed as:

                        y = m*x + C

                        m = -2/3

                        y = -2*x / 3 + C

                        1 = -2*9 / 3 + C ....... ( 9 , 1 )

                        C = 7

- The equation of the line is:

                        y = -2*x / 3 + 7