Answer:
Options (1), (2), (3) and (4)
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.