Question

A’ (4,-1) is the image of A after a translation along the vector (0,-6). What are the coordinates What are the coordinates of A?

Answer 1

The coordinates of A are ( 4 , 5 )

Further explanation

There are several types of transformations:

1. Translation
2. Reflection
3. Rotation
4. Dilation

Let us now tackle the problem!

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This problem is about Translation.

Properties of Translation of the images compared to pre-images:

• preserve Side Length
• preserve Orientation
• preserve Collinearity
• preserve Betweenness of Points
• preserve Angle Measurement

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Given :

The image of coordinates A = A' = ( 4 , - 1 )

The translation vector is ( 0 , - 6 )

Let:

A = ( x , y )

$A \overset{(a,b)}{\rightarrow} A'$

$( x , y ) \overset{(a,b)}{\rightarrow} ( x + a , y + b )$

$( x , y ) \overset{(0,-6)}{\rightarrow} ( x + 0 , y - 6 )$

$( x , y ) \overset{(0,-6)}{\rightarrow} ( x , y - 6 ) = ( 4 , - 1 )$

x = 4

y - 6 = - 1

y = -1 + 6

y = 5

A = ( x , y ) = ( 4 , 5 )

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Conclusion :

The coordinates of A are ( 4 , 5 )

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Transformation

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle , Vector , Image , Pre-Image , Coordinates

Answer 2

Answer:

The coordinates of A are (4,5)

Step-by-step explanation:

we know that

The translation is along the vector (0,-6)

so

The rule of the translation is

(x,y) ------> (x,y-6)

That means -----> The translation is 6 units down

A(x,y) ------> A'(x,y-6)

A'(4,-1)

therefore

A'(x,y-6)=A'(4,-1)

x=4

y-6=-1 -----> y=-1+6 ----> y=5

The coordinates of A are (4,5)