Question

Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.

On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?

(–2, 4)
(4, 2)
(2, –4)
(–4, –2)

Answer 1

Answer:

(2, –4)

Step-by-step explanation:

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Answer 2

Function transformation involves changing a function to another by obeying some transformation rules. The coordinate of pre-image of F' is

$F = (2,-4)$

Given that:

$F' = (4,-2)$

Figure ABCDEF is reflected across $y = -x$ to get A'B'C'D'E'F'

The rule of transformation is:

$(x,y) \to (-y,-x)$

This means that:

$(x,y) \to (-y,-x) = (4,-2)$

By comparison:

$-y = 4$

$-x = -2$

Solve for x and y

$y =-4$

$x =2$

Hence, the coordinate of pre-image of F' is

$F = (2,-4)$

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