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 1, negative 3), (1, 1), (2, negative 5). A blue triangle has the following vertices: (negative 4, 1), (negative 2, 5), (negative 1, negative 1).
Question content area bottom
Part 1
The translation rule is (x,y)right arrow(xplus(
enter your response here),yplus(
enter your response here)).
-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 1, negative 3), (1, 1), (2, negative 5). A blue triangle has the following vertices: (negative 4, 1), (negative 2, 5), (negative 1, negative 1).
Question content area bottom
Part 1
The translation rule is (x,y)right arrow(xplus(
enter your response here),yplus(
enter your response here)).
Answers
GPT-4o mini
To describe the translation from the black triangle to the blue triangle, we'll find the horizontal and vertical shifts for the x and y coordinates of the vertices.
The given vertices of the black triangle are:
1. \((-1, -3)\)
2. \((1, 1)\)
3. \((2, -5)\)
The corresponding vertices of the blue triangle are:
1. \((-4, 1)\)
2. \((-2, 5)\)
3. \((-1, -1)\)
Now we will calculate the translation for each vertex:
1. From \((-1, -3)\) to \((-4, 1)\):
- Change in x: \(-4 - (-1) = -4 + 1 = -3\)
- Change in y: \(1 - (-3) = 1 + 3 = 4\)
2. From \((1, 1)\) to \((-2, 5)\):
- Change in x: \(-2 - 1 = -3\)
- Change in y: \(5 - 1 = 4\)
3. From \((2, -5)\) to \((-1, -1)\):
- Change in x: \(-1 - 2 = -3\)
- Change in y: \(-1 - (-5) = -1 + 5 = 4\)
In all cases, we have the same translation:
- The x-coordinates are translated by \(-3\).
- The y-coordinates are translated by \(4\).
Thus, the translation rule is:
\((x,y) \rightarrow (x - 3, y + 4)\).
The given vertices of the black triangle are:
1. \((-1, -3)\)
2. \((1, 1)\)
3. \((2, -5)\)
The corresponding vertices of the blue triangle are:
1. \((-4, 1)\)
2. \((-2, 5)\)
3. \((-1, -1)\)
Now we will calculate the translation for each vertex:
1. From \((-1, -3)\) to \((-4, 1)\):
- Change in x: \(-4 - (-1) = -4 + 1 = -3\)
- Change in y: \(1 - (-3) = 1 + 3 = 4\)
2. From \((1, 1)\) to \((-2, 5)\):
- Change in x: \(-2 - 1 = -3\)
- Change in y: \(5 - 1 = 4\)
3. From \((2, -5)\) to \((-1, -1)\):
- Change in x: \(-1 - 2 = -3\)
- Change in y: \(-1 - (-5) = -1 + 5 = 4\)
In all cases, we have the same translation:
- The x-coordinates are translated by \(-3\).
- The y-coordinates are translated by \(4\).
Thus, the translation rule is:
\((x,y) \rightarrow (x - 3, y + 4)\).