The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
What is the transformation rule for reflection?
The transformation rules for reflection are:
Reflection at y-axis: y = f(-x);
Reflection at x-axis: y = -f(x);
Calculation:
The given polygon has four vertices EFGH.
Their coordinates are:
E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)
When the transformation rule: reflection across the y-axis is applied, the coordinates become:
y = f(-x); rule
For E(-4, -1), x-coordinate is -4. So, -(-4) = 4
⇒ E'(4, -1)
For F(-2, -1), x-coordinate is -2. So, -(-2) = 2
⇒ F'(2, -1)
For G(-1, -2), x-coordinate is -1. So, -(-1) = 1
⇒ G'(1, -2)
For H(-1, -4), x-coordinate is -1. So, -(-1) = 1
⇒ H'(1, -4)
Thus, the transformed coordinates are:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
Learn more about the reflection across the y-axis here:
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