Activity Point \( A(-3 ; 1) \) is shown on a coordinate pind alongside. Write down the coordinates and the quadrant of the image \( A^{\prime}(-3 ; 1) \) if point \( A \) translated as follows. a 1 unit upwards b 4 units to the right

To solve this problem, we need to understand how to translate a point on a coordinate plane. When a point is translated, its coordinates are shifted in a specific direction and distance. Let's go through each part of the problem step by step. ### Part a: 1 unit upwards When a point is translated 1 unit upwards, the y-coordinate increases by 1, while the x-coordinate remains the same. Given point \( A(-3, 1) \): - The x-coordinate remains \(-3\). - The y-coordinate increases by 1, so it becomes \(1 + 1 = 2\). Therefore, the image \( A' \) after translating 1 unit upwards is: \[ A'(-3, 2) \] Since the x-coordinate remains negative and the y-coordinate is positive, the point \( A' \) is in the **second quadrant**. ### Part b: 4 units to the right When a point is translated 4 units to the right, the x-coordinate increases by 4, while the y-coordinate remains the same. Given point \( A(-3, 1) \): - The y-coordinate remains \(1\). - The x-coordinate increases by 4, so it becomes \(-3 + 4 = 1\). Therefore, the image \( A' \) after translating 4 units to the right is: \[ A'(1, 1) \] Since both the x-coordinate and the y-coordinate are positive, the point \( A' \) is in the **first quadrant**. ### Summary - For part a (1 unit upwards): - Coordinates of \( A' \): \((-3, 2)\) - Quadrant: Second quadrant - For part b (4 units to the right): - Coordinates of \( A' \): \((1, 1)\) - Quadrant: First quadrant