If the point (8, 6) is the result of the composition /, what are the coordinates of the point prior to the composition? a. (–11, –9) b. (–8, –3) c. (–8, 6) d. (–5, –3)

Solution:

The given point on the coordinate plane = (8,6)

Following Composition can take place

1. Reflection and

2. Translation

3. Reflection and then Translation

4. Translation and then Reflection

Supposing ,(8,6)=Pre image

1. Reflection along X axis

Pre-image(8,6) changes to Image (8,-6)

2. Reflection along Y axis

Pre-image(8,6) changes to Image (-8,6)

If either translation or  (Reflection and then Translation)or (Translation and then Reflection),  i.e in the Pre-image (8,6) has taken place i.e Translation by same amount ( in Horizontally right or left and in vertically up or down has taken place),and then reflection or if reflection has taken place in the beginning and then Translation,  it does not take us to any of the three options i.e A. (–11, –9) B. (–8, –3)  D. (–5, –3).

So, if the point i.e Image (8,6) is the result of the composition, the coordinates of the point prior to the composition will be (-8,6) i.e Pre image, among the option provided  is Option (C), when point(-8,6) is reflected along positive Y axis results in point (8,6).

the answer is b.

step-by-step explanation:

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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