Question

Translation 3 units left and 15 units down

Rotation 270° counterclockwise around the origin

Answer 1

Original image:

W = (14, 10)

X = (12, 4)

Y = (6, 6)

Z = (8, 12)

To translate 3 units left, subtract 3 from the x-values (x - 3)

To translate 15 units down, subtract 15 from the y-values (y - 15)

W' = (14 - 3, 10 - 15) = (11, -5)

X' = (12 - 3, 4 - 15) = (9, -11)

Y' = (6 - 3, 6 - 15) = (3, -9)

Z' = (8 - 3, 12 - 15) = (5, -3)

(red square on attachment)

To rotate 270° counterclockwise around the origin (0, 0),

the point (x, y) becomes (y, -x). So, switch x and y and make x negative.

W'' = (-5, -11)

X'' = (-11, -9)

Y'' = (-9, -3)

Z'' = (-3, -5)

(green square on attachment)

Answer 2

W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)

Kindly check the attached image for more reference

Explanation:

Given points of WXYZ ( can be identified by looking at the graph )

• W : (14,10)

• X : (12,4)

• Y : (6,6)

• Z : (8,12)

Applying translation 3 units left , 15 units down

(Note when shifting left , you subtract from the x value , when shifting down, you subtract from the y value.)

Rule for translation (x,y) ===> ( x - 3 , y - 15 )

Applying translation to given points

• W : (14,10) ===> (14-3,10-15) ===> (11,-5)
• X : (12,4) ===> (12-3,4-15) ===> (9,-11)
• Y : (6,6) ===> (6-3,6-15) ===> (3,-9)
• Z : (8,12) ===> (8-3,12-15) ===> (5,-3)

Applying rotation 270° counterclockwise around the origin

Rotation 270° clockwise rule : (x,y) ===> (y,-x)

Explanation of rule , change the sign of the x values, then swap the x and y values places.

Applying rotation rule to points

• W : (11,-5) ===> (y,-x) ===> (-5,-11)

• X : (9,-11) ===> (y,-x) ===> (-11,-9)
• Y : (3,-9) ===> (y,-x) ===> (-9,-3)
• Z : (5,-3) ===> (y,-x) ===> (-3,-5)

So the final points of square WXYZ after the two transformations would be W'' (-5,-11) , X'' (-11,-9) , Y'' (-9,-3) and Z'' (-3,-5)

To see this graphed, kindly view the attached image.

The red square represents the square before any transformations

The blue square represents the square following the translation

And the black square represents the coordinates of the square after the full transformation including both the translation and the rotation .