A, B, and C are collinear, and B is between A and C. The ratio of AB is 1:1. If A is at (1,-9) and B is at (2,0), what are the coordinates of point C

Accepted Solution

Answer:(3,9)Step-by-step explanation:So I drew a right triangle with the line segment A(1,-9) to C[tex](a,b)[/tex] as the hypotenuse.  This line segment does contain point B(2,0). This is shown in the picture.We want to find a point C[tex](a,b)[/tex] so that AB to BC has a ratio of 1:1. So this means B is the midpoint really.So if we averaged the endpoints of the line segment it would equate to point B.That is:[tex]\frac{1+a}{2}=2[/tex] and [tex]\frac{-9+b}{2}=0[/tex]Multiply both sides by 2:[tex]1+a=4[/tex] and [tex]-9+b=0[/tex]The first equation can be solved by subtracting 1 on both sides giving [tex]a=3[/tex].The second equation can be solved by adding 9 on both sides giving[tex]b=9[/tex].Point C is (3,9).