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------------------------------------------------ The coordinate grid shows a pentagon. The pentagon is translated 3 units to the right and 5 units up to create a new pentagon. What is the rule for the location of the new pentagon?

Step-by-step explanation: Given in the question a pentagon on the coordinate plane. It is translated 3 units to the right and 5 units up to create a new pentagon. We are to find the rule for the location of the new pentagon.

Let (x,y) represents any vertex of the pentagon. Since, we are to translate 3 units to the right, so we need to add 3 units to the x-coordinate of every vertex. And also, since we are to translate 5 units up, so we must add 5 units to the y-coordinate of every vertex.

Therefore, every vertex (x,y) should be changed to (x+3,y+5) to get the new pentagon.

Thus, the required rule for the location of new pentagon is (x,y) ⇒ (x+3,y+5).

For example, the vertices of the given pentagon are (-1,3), (2,2), (5,3), (4,6) and (1,5). After the translation, the vertices of the new pentagon will be

(2,8), (5,7), (88), (7,11) and (4,10).