Question

The blue figure is a translation image of the black figure. Write a rule to describe the translation.
-6
-3
3
6
-6
-3
3
6
x
y



A coordinate system has a horizontal x-axis and a vertical y-axis each labeled from negative 6 to 6 in increments of 1. A black triangle has the following vertices: (negative 4, negative 1), (negative 1, 3), (2, negative 3). A blue triangle has the following vertices: (negative 5, 1), (negative 2, 5), (1, negative 1).
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Part 1
The translation rule is ​(x,y)right arrow​(xplus​(
  
enter your response here​),yplus​(
  
enter your response here​)).

Answer 1

To determine the translation rule between the black triangle and the blue triangle, we need to find the change in the x-coordinates and the change in the y-coordinates for each corresponding vertex in the two triangles.

Let's compare the vertices:

1. Black triangle vertex: \((-4, -1)\) corresponds to Blue triangle vertex: \((-5, 1)\)
- Change in x: \(-5 - (-4) = -5 + 4 = -1\)
- Change in y: \(1 - (-1) = 1 + 1 = 2\)

2. Black triangle vertex: \((-1, 3)\) corresponds to Blue triangle vertex: \((-2, 5)\)
- Change in x: \(-2 - (-1) = -2 + 1 = -1\)
- Change in y: \(5 - 3 = 2\)

3. Black triangle vertex: \((2, -3)\) corresponds to Blue triangle vertex: \((1, -1)\)
- Change in x: \(1 - 2 = -1\)
- Change in y: \(-1 - (-3) = -1 + 3 = 2\)

From the calculations, we observe that:
- The x-coordinate decreases by 1:
\[
x + (-1) \quad \text{or simply} \quad x - 1
\]

- The y-coordinate increases by 2:
\[
y + 2
\]

Therefore, the translation rule is:
\[
(x, y) \rightarrow (x - 1, y + 2)
\]

So the final answer for the translation rule is:
\[
(x,y) \rightarrow (x - 1,y + 2)
\]