Find the x-value for point C such that AC and BC from a 2:3 ratio.

Given:

Point C divides AB such that AC:BC=2:3.

To find:

The x-value for point C.

Solution:

Section formula: If a point divide a line segment in m:n, then

Form the given graph it is clear that the endpoints of the line segment AB are A(-3,5) and B(3,0).

Point C divides AB such that AC:BC=2:3. Using section formula, the coordinates of point C are

The x-value of C is -0.6.

Therefore, the correct option is B.

I think the second way is better
there are squares,so
1st way
JH=4
HF=2*4=8 
from right triangle HFG
2*(HG)² =HF² by Pythagorean theorem 
2*(HG)² =8² , (HG)² =32  
also (HG)²=32 is the area of the small square

(JH/JC)²= A(small square)/A(large square)
(4/9)²=32/A(large square)
4²/9²=32/A
A(large square)=(9²*32)4² =81*32/16=162

162-32=130 cm²    of the shaded area

2d way
 from triangle JHG
4²+4²= 32 (side of small square)² ---Hypotenuse ², at the same time the area of the small square
from triangle JDC
9²+9²= 162(side of large square)² hypotenuse² of the large triangle, at the same time the area of the large square
shaded area 162-32=130