Question

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Answer 1

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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