If a point has the coordinates (5, -3), which axis is it closer to: the x-axis or the y-axis? Justify your answer.

To determine which axis the point **(5, -3)** is closer to—the **x-axis** or the **y-axis**—we can calculate the perpendicular distance from the point to each axis. ### Distance to the **x-axis** The distance from a point to the x-axis is determined by the absolute value of its **y-coordinate**. \[ \text{Distance to x-axis} = |y| = |-3| = 3 \text{ units} \] ### Distance to the **y-axis** Similarly, the distance from a point to the y-axis is determined by the absolute value of its **x-coordinate**. \[ \text{Distance to y-axis} = |x| = |5| = 5 \text{ units} \] ### Comparison - **Distance to x-axis**: **3 units** - **Distance to y-axis**: **5 units** Since **3 units** (distance to the x-axis) is less than **5 units** (distance to the y-axis), the point **(5, -3)** is **closer to the x-axis**. ### Visual Representation Here's a simple diagram to illustrate: ``` y | | (5, -3) | * | |_________________ x ``` - The point (5, -3) is **3 units** away vertically from the x-axis. - It is **5 units** away horizontally from the y-axis. Therefore, the point is closer to the **x-axis**.