What coordinate will both people walk through

Question

Gina and Marissa each walk in a straight line between two points. Using the points on a map that the girls created, Gina will start at (–6, –10) and will stop at (3, –1). Marissa will start at (4, –9) and will stop at (–4, 7). At what point will Gina and Marissa both walk through?

Answer 1

The point we are looking for is the point of intersection of two lines.  

 

First line:  slope = [-1-(-10)]/[3-(-6)] = 9/9 = 1 = m

 

               Equation of line:  y = mx + b

 

                                        y = x + b  

 

                                        Since (3,-1) is on the line, -1 = 3+b

 

                                                                              b = -4

 

                                        Equation of first line:  y = x - 4

 

Second line:  slope = [7 - (-9)]/[-4 - 4] = 16/(-8) = -2 = m

 

                 Equation of line:  y = -2x + b

 

                                         Since (-4,7) is on the line, 7 = -2(-4) + b

 

                                                                              b = -1

 

                                         Equation of second line:  y = -2x - 1

 

The lines intersect when -2x-1 = x - 4

 

                                      -3x = -3

 

                                        x = 1   and y = -2(1) - 1 = -3

 

Gina and Marissa both walk through the point (1,-3).