Question

A(-3,-3) A is a glide reflection where the translation is (x,y) (x+5,y), and the line of reflection is y=1. what are the coordinates of A

Answer 1

Answer:

Glide Reflection: It is a composition of transformations.

In glide reflection, a translation is first performed on the figure then it is reflected over a line.

Given:

The coordinate of A = (-3,-3)

The rule of translation is $(x,y) \rightarrow (x+5 , y)$ and the line of reflection is y=1.

Now,

First applying the rule of translation we get;

$A(-3, -3) \rightarrow (-3+5, -3)$ = (2 , -3)

Since, -3 which is 4 unit below the line of reflection,

then,

after the reflection, over the line  y=1 we get, the reflected point A' would be 4 units above the line of reflection

so, A' (2, 1+4) =(2,5)

Therefore, the coordinate of A' (2,5).

Answer 2

The coordinates of A is $\boxed{\left( {2,5} \right)}.$

Further explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Explanation:

The translation mapping of a single translation can be expressed as follows,

$\left( {x,y} \right) \Rightarrow \left( {x + h,y + k} \right)$

Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.

The coordinates of A after reflection is $\boxed{\left( {2,5} \right)}.$

The translation rule is $\left( {x,y} \right) \to \left( {x + 5,y} \right)$

The coordinates after translation can be obtained as follows,

A $\left( { - 3,3} \right) \to \left( { - 3 + 5, - 3} \right) = \left( {2, - 3} \right)$

The reflection is along $y = 1$. Therefore, only y-coordinate will change and the x-coordinate remain the same.

-3 is 4 units below the reflection line $y = 1.$

Therefore, the coordinate of A after reflection can be obtained as follows,

A $\left( {2,1 + 4} \right) = \left( {2,5} \right)$

Hence,the coordinates of A is $\boxed{\left( {2,5} \right)}$.

Kindly refer to the image attached.

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides, A(-3,-3), glide reflection, (x,y), (x+5,y), the line of reflection is y=1, coordinates of A.