Question

X'Y'Z' is the dilation of triangle XYZ. What is the value of a? TIP: Create an equation using the scale factor ratios. Scale Factor= Image Value / Original Value

Answer 1

Answer:

I think I have thought this through but I have not completed all the maths.

I let XYZ be circumscribed by a circle of radius 3 (I find it easier to use actual numbers)

area Triangle XGY = 0.5*3*3sin120 =(9sqrt3)/4

area Triangle X'GY' = 2/3 of that = (3sqrt3)/2

Now find the area of one little triangle.

the equation of XZ is y=sqrt3x+3

point A has a y value of 1 so the x value is (-2sqrt3)/3

Y' is the intersection of x^2+y^2=4 and y=1 so I think it is (-sqrt3,1)

Distance AY'= sqrt3/3

So from that you can work out the area of each of the little triangles.

Then you can work out the rest.

(maybe there is a better way, but that will work)

You will need to check all my logic and arithmetic.