Select all that apply. Describe the transformations. 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.

Answer: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 unitsRule 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.Step-by-step explanation: