Question

PLEASE HELP!!!!

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. Sample Response: Translations move every point on a figure the same distance and direction. You can use the one vertex and its image to find the rule that maps the triangle to its image. This rule can then be used to find the images of the other vertices of the triangle. Plot the vertices and connect them to form the image of the triangle. What did you include in your response? Check all that apply. Translations move every point the same distance and direction. Use the given image to determine the translation rule. Plot the remaining vertices using the rule.

Answer 1

Translations move every point the same distance and direction.

Use the given image to determine the translation rule.

Plot the remaining vertices using the rule.

Answer 2

When a triangle is translated, it means the triangle is moved away from its original position.

When the coordinates of a triangle, and the coordinate of only one point of the image are given, the translation rule is calculated by subtracting the coordinates of the pre-image from the image.

From the question, we understand that:

The vertices of the triangle are known. Assume they are:

\begin{gathered}A= (1,1)\\ B = (3,5) \\ C = (4,-1)\end{gathered}A=(1,1)B=(3,5)C=(4,−1)

The vertex of one of the image is also known. Assume the point is:

A' = (3,-1)A′=(3,−1)

To calculate the translation rule;

We simply subtract the vertices of the image from the pre-image.

In this case, the translation rule would be:

T < x,y > = A' - AT<x,y>=A′−A

So, we have:

T < x,y > = (3,-1) - (1,1)T<x,y>=(3,−1)−(1,1)

Rewrite as:

T < x,y > = (3 -1 ,-1 - 1)T<x,y>=(3−1,−1−1)

T < x,y > = (2 ,-2)T<x,y>=(2,−2)

So, the translation rule is:

T_{ < x,y > } (x,y) \to (x + 1, y - 1)T<x,y>(x,y)→(x+1,y−1)

Hence, the translation rule can be derived by subtracting the coordinates of the pre-image from the image.