The images of the transformations are (-1, 2), (-1, 0), (-5, 0) and (-2, 3), (-2, -4), (-1, 0), (3, 0) and (3, -4), (-4, -2), (-4, 2) and (-2, 0) & (-1, 1), (1, 3), (3, 0) and (1, -1)
The value of x on both lines is 10
How to perform the transformations
Transformation 1
The coordinates are given as
(1, -2), (1, 0), (5, 0) and (2, -3)
The transformation is given as
Rotation 180 degrees
This rule is represented as
(x, y) ⇒ (-x, -y)
So, we have
(-1, 2), (-1, 0), (-5, 0) and (-2, 3)
See attachment for the image of the transformation
Transformation 2
The coordinates are given as
(-4, 0), (-3, 4), (1, 4) and (1, 0)
The transformation is given as
Translation 2 units right and 4 units down
This rule is represented as
(x, y) ⇒ (x + 2, y - 4)
So, we have
(-2, -4), (-1, 0), (3, 0) and (3, -4)
See attachment for the image of the transformation
Transformation 3
The coordinates are given as
(3, 0), (3, 4), (5, 2)
The transformation is given as
Translation 7 units left and 2 units down
This rule is represented as
(x, y) ⇒ (x - 7, y - 2)
So, we have
(-4, -2), (-4, 2), (-2, 0)
See attachment for the image of the transformation
Transformation 4
The coordinates are given as
(-1, -1), (-3, 1), (0, 3), (1, 1)
The transformation is given as
Rotation 90 degrees clockwise
This rule is represented as
(x, y) ⇒ (y, -x)
So, we have
(-1, 1), (1, 3), (3, 0), (1, -1)
See attachment for the image of the transformation
The values of x on the lines
Lines 1
By the vertical angle theorem, we have
6x = 60
Divide by 6
x = 10
Lines 2
By the theorem of corresponding angles, we have
2 + 4x = 42
This gives
4x = 40
Divide by 4
x = 10
Hence, value of x is 10
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