Question

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

Answer 1

Since the heights are same, the ratio of areas equals the ratio of bases :
\[\dfrac{3}{4} = \dfrac{AC}{BC}\]

Answer 2

so you need to find the point C such that it divides AB in ratio 3:4

Answer 3

A = (1, -9)
B = (8, -2)

ratio is 3 : 4

use section formula and find the point C

Answer 4

http://www.onlinemath4all.com/images/2.gif

\[C = \left(\frac{3(8) + 4(1)}{3+4},~\frac{3(-2)+4(-9)}{3+4}\right)=(4,~-6)\]