Select all that apply. Describe the transformations.

(Look at image!)

The yellow circle was translated left 2 units and up 2 units.
The yellow circle was reflected over both axes.
The yellow circle was reflected over the y-axis and translated up 2 units.
The yellow circle was reflected over the x-axis and translated left 2 units.

Options (1), (2), (3) and (4)

Step-by-step explanation:

Two circles (yellow and blue) with their centers as (1, -1) and (-1, 1) have been given in picture.

Now we will check each option for the transformations of these points.

Option (1)

The yellow circle was translated left by 2 units and up by 2 units.

Then rule for translation will be,

(x, y) → [(x - 2), (y + 2)]

Following this rule (1, -1) will become,

(1, -1) → [(1 - 2), (-1 + 2)]

        → (-1, 1)

But the center of blue circle after translation is (-1, 1),

Therefore, this option will be the answer.

Option (2)

The yellow circle was reflected over both axis.

If (1, -1) is reflected over x-axis,

Rule to be followed,

(x, y) → (x, -y)

Followed by reflection over the y-axis,

rule for the reflection,

(a, b) → (-a, b)

By this rule, (x, -y) will become,

(x, -y) → (-x, -y)

By these transformations (1, -1) will become

(1, -1) → ( -1, 1)

By these transformations image of yellow circle is the blue circle.

Option (2) is the answer.

Option (3)

The yellow circle was reflected over the y-axis and translated up by 2 units.

Rule for reflection over y-axis,

(x, y) → (-x, y)

followed by the translation 2 units up,

(-x, y) → (-x, y+2)

By these transformations,

(1, -1) → (-1, 1)

Therefore, option (3) is the correct option.

Option (4)

The yellow circle was reflected over the x-axis and translated left 2 units

Rule for reflection over x-axis,

(x, y) → (x, -y)

Followed up by the translation of 2 units left.

(x, -y) → (x - 2, -y)

By this rule point (1, -1) will become,

(1, -1) → [(1 - 2), -(-1)]

        → (-1, 1)

Which is the center of blue of circle.

Therefore, Option (4) will be the answer.

All given options are correct.

the answer is 15.50 for one mile

b) is slope: 0   y- intercept 15.5