Asked by Hannah
                1. A, B and C are collinear, and B is between A and C. The ratio of AB to AC is 3:4. If A is at (-8,1) and B is at (-2,-2), what are the coordinates of C?
2. The segment joining (1,-3) and (4,-6) is extended a distance equal to one-sixth of its own length. Find the terminal point.
I solved these two problems yet neither of them is correct.
            
        2. The segment joining (1,-3) and (4,-6) is extended a distance equal to one-sixth of its own length. Find the terminal point.
I solved these two problems yet neither of them is correct.
Answers
                    Answered by
            oobleck
            
    AB:AC = 3:4 means that B is 3/4 of the way from A to C.
Think about it. Start at A. When you get to B, AB is 3/4 of the whole distance AC.
B = A + k (C-A)
when k=0, you are at A
when k=1, you are at C
Bx = Ax + 3/4 (Cx - Ax) = -8 + 3/4 (-2+8) = -8 + 3/4 (6) = -7/2
That is, the distance from -8 to -2 is 6. 3/4 of 6 = 9/2
By = 1 + 3/4 (-2-1) = 1 + 3/4 (-3) = -5/4
For #2, If we let A = (1,-3) and B = (4,-6), we want C such that BC = 1/6 AB
That is, AC:AB = 7/6
Cx = Ax + 7/6 (Bx - Ax) = 1 + 7/6 (4-1) = 9/2
Cy = -3 + 7/6 (-6+3) = -3 + 7/6 (-3) = -13/2
So, C = (9/2, -13/2)
You really should get out some graph paper and plot the points, to make sure your answer satisfies the conditions. It may be easier to see geometrically.
    
Think about it. Start at A. When you get to B, AB is 3/4 of the whole distance AC.
B = A + k (C-A)
when k=0, you are at A
when k=1, you are at C
Bx = Ax + 3/4 (Cx - Ax) = -8 + 3/4 (-2+8) = -8 + 3/4 (6) = -7/2
That is, the distance from -8 to -2 is 6. 3/4 of 6 = 9/2
By = 1 + 3/4 (-2-1) = 1 + 3/4 (-3) = -5/4
For #2, If we let A = (1,-3) and B = (4,-6), we want C such that BC = 1/6 AB
That is, AC:AB = 7/6
Cx = Ax + 7/6 (Bx - Ax) = 1 + 7/6 (4-1) = 9/2
Cy = -3 + 7/6 (-6+3) = -3 + 7/6 (-3) = -13/2
So, C = (9/2, -13/2)
You really should get out some graph paper and plot the points, to make sure your answer satisfies the conditions. It may be easier to see geometrically.
                    Answered by
            Kristine Morales
            
    (0,-3)
    
                    Answered by
            Joanna
            
    I checked, its (0, -3)
    
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.