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

I hope this helps you

Answer 2

(1/2(AC) * DC) / (1/2(BC) * DC) = 3/4
AC / BC = 3/4

The coordinate of C be (x, y), then
((4(1) + 3(8))/7, (4(-9) + 3(-2))/7) = ((4 + 24)/7, (-36 - 6)/7) = (28/7, -42/7) = (4, -6)