The coordinates of A is [tex]\boxed{\left( {1,10} \right)}.[/tex]
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,
[tex]\left( {x,y} \right) \Rightarrow \left( {x + h,y + k} \right)[/tex]
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 [tex]\boxed{\left( {- 5,- 4} \right)}.[/tex]
The translation rule is [tex]\left( {x,y} \right) \to \left( {x + 6,y}\right)[/tex]
The coordinates after translation can be obtained as follows,
[tex]A\left( { - 5,- 4} \right) \to \left( { - 5 + 6, - 4} \right) = \left( {1, - 4} \right)[/tex]
The reflection is along [tex]y = 3[/tex]. Therefore, only y-coordinate will change and the x-coordinate remain the same.
-4 is 7 units below the reflection line [tex]y = 3.[/tex]
Therefore, the coordinate of A after reflection can be obtained as follows,
[tex]A\left( {1,3 + 7} \right) = \left( {1,10} \right)[/tex]
Hence, the coordinates of A is [tex]\boxed{\left( {1,10} \right)}.[/tex]
Kindly refer to the image attached.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides, glide reflection, (x,y), (x+6,y), the line of reflection is y=1, coordinates of A.
