Point A (2, 6) has been translated 1 left and 3 up followed by a 180 degree rotation. What is the image of Point A?

Step-by-step explanation:

Given

Point: A(2,6)

Translation: 1 left and 3 up

Rotation: 180 degrees

Required

Image of Point A

Taking the exercise one after the other

Represent the function as: (x,y)

Such that

1 unit left translation means the function becomes (x - 1, y)

2 unit up translation means the function becomes (x - 1, y + 2)

Applying the above transformation

At this stage, the coordinate becomes

When a function (x,y) is rotated by 180, the new function becomes (-x,-y)

So;

The further transformation of A is

Hence, the new image of A is

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.