Question

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

A (3,-7)
B. (5,-5)
C. (7,-3)
D. (4,-6)

Answer 1

Answer: I think its C

Explanation:

Answer 2

The coordinate of point C is (4 , - 6) .

Explanation:

Given as ;

The Δ ADC and The Δ DCB are divided in the ratio = m : n = 3 : 4

The coordinate of point A =
`x_1 , y _1` = 1 , - 9

The coordinate of point B =
`x_2 , y _2` = 8 , -2

Let The coordinate of point C = x , y

Now, According to question

x =
`(m * x_2 + n* x_1)/(m + n)`

Or, x =
`(3 * 8 + 4* 1)/(3 + 4)`

Or, x =
`(24 + 4)/(7)`

∴ x =
`(28)/(7)`

i.e x = 4

Similarly

y =
`(m * y_2 + n* y_1)/(m + n)`

Or, y =
`(3 * (-2) + 4* (-9))/(3 + 4)`

Or, y =
`( - 6 - 36)/(7)`

∴ y =
`(- 42)/(7)`

i.e y = - 6

So, The coordinate of point C = x , y = 4 , - 6

Hence,The coordinate of point C is (4 , - 6) . Answer