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)

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. (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)                   (x, -y)

A(-3, 5)                       A'(-3, -5)

B(2, 8)                       B'(2, -8)

C(-4, -5)                    C'(-4, 5)

Therefore, the correct option is option D.

Learn more about the reflection transformation here:

link

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

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.

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step-by-step explanation:

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