Enter your answer and show all the steps that you use to solve this problem.
At the halftime show, a marching band marched in formation. The lead drummer started at a point with coordinates (−2,−5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. What were the coordinates of the drummer's final position?
a. The rule to describe the translation is (x, y) → (x + 1, y + 3).
b. The coordinates of the drummer's final position are (−1, −2).
To solve this problem, we can use the rule of translation. The rule of translation states that when an object is translated, the coordinates of the object change by the same amount in each direction. In this problem, the lead drummer moved 3 steps up and 1 step right. This means that the x-coordinate increased by 1 and the y-coordinate increased by 3. Therefore, the rule of translation for this problem is (x, y) → (x + 1, y + 3).
Using this rule, we can calculate the coordinates of the drummer's final position. The drummer started at the point (−2, −5). Applying the rule of translation, we can calculate the coordinates of the drummer's final position as (−2 + 1, −5 + 3) = (−1, −2). Therefore, the coordinates of the drummer's final position are (−1, −2).