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You are given the coordinates of a triangle and coordinates for only one of the vertices of its image under a translation. Explain how to translate the entire triangle

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sqdancefan
For the known image point, subtract the coordinates of the corresponding original point. To find the other image points, add that difference to each of the corresponding original points.

Given A and A', compute D = A' - A. The you have
  B' = B + D
  C' = C + D


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Perform the arithmetic on corresponding coordinates. (dx, dy) = (ax' - ax, ay' - ay)
MrRoyal

Translation involves moving a shape away from its original position.

To translate the entire triangle, you need to

  1. Get the translation rule
  2. Apply the translation rule

From the question, we understand that:

  • The coordinates of the triangle are known
  • The coordinates of one of the vertices of the image is known

Assume that, the coordinates of the triangle is as follows  

[tex]\mathbf{A = (4,6)}\\\mathbf{B = (5,4)}\\\mathbf{C = (3,0)}[/tex]

Assume one of the vertices of the image is:  

[tex]\mathbf{A' = (2,1)}[/tex]

The first thing to do is to calculate the translation rule using the vertex of the image and the corresponding vertex of the pre-image

This is represented as:

[tex]\mathbf{(x,y) = A' - A}[/tex]

[tex]\mathbf{(x,y) = (2,1) - (4,6)}[/tex]

[tex]\mathbf{(x,y) = (2 - 4,1 -6)}[/tex]

[tex]\mathbf{(x,y) = (- 2,-5)}[/tex]

So, the translation rule is:

[tex]\mathbf{(x,y) \to (x- 2,y-5)}[/tex]

Apply the translation rule on other points

[tex]\mathbf{B' = (5-2,4-5)}[/tex]

[tex]\mathbf{B' = (3,-1)}[/tex]

[tex]\mathbf{C' = (3-2,0-5)}[/tex]

[tex]\mathbf{C' = (1,-5)}[/tex]

So, the step to translate the entire triangle is:

  • Calculate the translation rule
  • Apply the translation rule on other points

Learn more about translations at:

https://brainly.com/question/14090589

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