Triangle abc below is reflected across the y-axis and then translated 1 unit right and 2 units down.
a) write the coordinates of the vertices of the image after reflection.
b) write a rule for the translation. use arrow notation.
c) write the coordinates of the vertices of the new image after translation.

The correct answers are: A) A'(-1, 3); B'(-4, 5); C'(-3, 1); B) <1, -2>, C) A''(0, 1); B''(-3, 3); C''(-2, -1).

Explanation:
When you reflect an image across the y-axis, it negates the x-coordinate. This means all of the x-coordinates will become the opposite sign after the reflection.

Since the translation is 1 unit right, that is adding 1 to the x-coordinate; since it is 2 units down, that is subtracting 2 from the y-coordinate. Once we add 1 to each x-coordinate and subtract 2 from each y-coordinate, we end up with the vertices listed above.

The coordinates of the vertices of the new image after translation and reflection :

A''(0, 1); B''(-3, 3); C''(-2, -1).

Further explanation

A reflection is an example of a transformation

Reflection is the process of mirroring each point on the geometry of a certain line.

The original figure is called the pre-image and the final figure is called the image

The image will be congruent with the pre image and the distance from the image to the mirror axis is the same as the distance from the pre image to the mirror axis

• The equation of reflection across the y-axis

x '= -x

y '= y

can be written

While the transformation itself is the displacement of the object given a distance and direction (for example up or down)

So each point is moved in the same distance and direction

Can be formulated :

A(x,y)⇒ T(a,b) ⇒ A'(x+a,y+b)(T=translated)

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.

So the stages

1.  reflected across the y-axis first and then

2. translated 1 unit right and 2 units down.(T(a,b) ⇒a=1,b=-2)

reflected across the y-axis

Coordinate A(1,3),B(4,5),C(3,1)

reflected becomes :

A(1,3)⇒A'(-1,3)

B(4,5)⇒B'(-4,5)

C(3,1)⇒C'(-3,1)

translated (T(a,b) ⇒a=1,b=-2)

A'(-1,3) ⇒A''(-1+1,3-2)⇒A"(0,1)

B'(-4,5) ⇒B''(-4+1,5-2)⇒A"(-3,3)

C'(-3,1) ⇒ C"(-3+1,1-2)⇒C"(-2,-1)

Learn more

Transformation from function

link

the rule for the reflection

link

the transformation rule

link

Keywords: reflection.,translation, the coordinates

Where’s the stuff st? ? lol sorry

Ithink it’s b, hope this .