Answer :
To determine the rule that describes the translation of a rectangle on a coordinate plane, we need to consider the effects of translating the rectangle 5 units up and 3 units to the left.
1. Translation 5 units up: When an object is translated upwards on a coordinate plane, its y-coordinate increases by the number of units it is moved. This means we need to add 5 to the y-coordinate of every point on the rectangle.
2. Translation 3 units to the left: When an object is translated to the left on a coordinate plane, its x-coordinate decreases by the number of units it is moved. This means we need to subtract 3 from the x-coordinate of every point on the rectangle.
Therefore, to find the new coordinates \((x', y')\) of a point \((x, y)\) after translating it 5 units up and 3 units to the left, we apply these transformations:
- New x-coordinate: \( x' = x - 3 \)
- New y-coordinate: \( y' = y + 5 \)
Thus, the rule that describes the translation can be written as:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
Examining the given options:
- \((x, y) \rightarrow (x + 5, y - 3)\)
- \((x, y) \rightarrow (x + 5, y + 3)\)
- \((x, y) \rightarrow (x - 3, y + 5)\)
- \((x, y) \rightarrow (x + 3, y + 5)\)
The correct rule matches:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
So, the rule that describes the translation of the rectangle 5 units up and 3 units to the left is:
[tex]\[ \boxed{(x, y) \rightarrow (x - 3, y + 5)} \][/tex]
1. Translation 5 units up: When an object is translated upwards on a coordinate plane, its y-coordinate increases by the number of units it is moved. This means we need to add 5 to the y-coordinate of every point on the rectangle.
2. Translation 3 units to the left: When an object is translated to the left on a coordinate plane, its x-coordinate decreases by the number of units it is moved. This means we need to subtract 3 from the x-coordinate of every point on the rectangle.
Therefore, to find the new coordinates \((x', y')\) of a point \((x, y)\) after translating it 5 units up and 3 units to the left, we apply these transformations:
- New x-coordinate: \( x' = x - 3 \)
- New y-coordinate: \( y' = y + 5 \)
Thus, the rule that describes the translation can be written as:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
Examining the given options:
- \((x, y) \rightarrow (x + 5, y - 3)\)
- \((x, y) \rightarrow (x + 5, y + 3)\)
- \((x, y) \rightarrow (x - 3, y + 5)\)
- \((x, y) \rightarrow (x + 3, y + 5)\)
The correct rule matches:
[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]
So, the rule that describes the translation of the rectangle 5 units up and 3 units to the left is:
[tex]\[ \boxed{(x, y) \rightarrow (x - 3, y + 5)} \][/tex]
