Find the ratio of the area of triangle xby to the area of triangle abc for the given measurements, if xy = 2, ac = 3 a. 1/3 b. 2/3 c. 4/9

(c)              

Step-by-step explanation:

Consider ΔXBY and ΔABC

∠XYB = ∠ACB    [ Corresponding angles of parallel line (AC and XY) are equal]

∠XBY = ∠ABC (Common angles)

By AA similarity, ΔXBY ΔABC,

We know that the ratio of area of two similar triangles is the square of ratios of their sides.

Ratio of sides =  

                       =  

=

                         =  

                        =

Option (c) is correct

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.