Question

What is the rule used to transform ΔABC to its image?

A(−3, 5), B(2, 8), C(−4, −5) and A'(−3, −5), B'(2, −8), C'(−4, 5)

A. Rm(x, y) = (−y, −x), where the equation of line m is y = −x
B. Rn(x, y) = (y, x), where the equation of line n is y = −x
C. Ry-axis(x, y) = (−x, y)
D. Rx-axis(x, y) = (x, −y)

Answer 1

Answer:

D

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

That is the x- coordinate remains unchanged while the y- coordinate is the negative of the original y- coordinate.

Given

A(- 3, 5 ) → A'(- 3, - 5 )

B(2, 8 ) → B'(2, - 8)

C(- 4, - 5 ) → C'(- 4, 5 )

The rule for reflection in the x- axis has been applied here → D

Answer 2

A reflection about a line is a transformation that forms an image as far behind the line as the object is in front

The correct option that gives the rule used to transform ΔABC to its image is option D.

D. $R_{x-axis}$(x, y) = (x, -y)

The reasons why the option D is correct is given as follows

The given coordinates are;

ΔABC; A(-3, 5), B(2, 8), C(-4, -5)

ΔA'B'C'; A'(-3, -5), B'(2, -8), C'(-4, 5)

The difference between the coordinates of ΔABC, and ΔA'B'C' is the change in the sign of the y-values of preimage in the form; (x, y) to (x, -y)

A transformation of (x, y) to (x, -y), is equivalent to a reflection across the x-axis

(x, y)  ${}$       $\underset \longrightarrow {R_{x-axis}}$           (x, -y)

A(-3, 5)          $\longrightarrow$             A'(-3, -5)

B(2, 8)           $\longrightarrow$             B'(2, -8)

C(-4, -5)         $\longrightarrow$            C'(-4, 5)

Therefore, the correct option is option D. $\underline {R_{x-axis}(x, y) = (x, -y)}$

Learn more about the reflection transformation here:

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