Question

In the diagram, the areas of and are in a ratio of 3 : 4. What are the coordinates of point C?

Answer 1

9514 1404 393

Answer:

  D.  (4, -6)

Step-by-step explanation:

Since the heights of both triangles are the same (CD), their areas are proportional to their bases. That is ...

  AC : CB = 3 : 4

In terms of coordinates, ...

  4(C -A) = 3(B -C) . . . . multiply the ratios by 4(CB)

  4C -4A = 3B -3C . . . .simplify

  7C = 4A +3B . . . . . . . isolate C

  C = (4A +3B)/7 . . . . . divide by 7

  C = (4(1, -9) +3(8, -2))/7 = (28, -42)/7 . . . . substitute given coordinates

  C = (4, -6)