In this exercise we use the Distance Formula,
Which of the points or is closer to the origin?
Point is closer to the origin.
Point is closer to the origin.
Points and are the same distance from the origin.

Ask by Fernandez Reyes. in the United States

Jan 22,2025

Question

In this exercise we use the Distance Formula,
Which of the points or is closer to the origin?
Point is closer to the origin.
Point is closer to the origin.
Points and are the same distance from the origin.

Ask by Fernandez Reyes. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To determine which point is closer to the origin $$(0, 0)$$, we'll use the **Distance Formula**:

$$
\text{Distance} = \sqrt{(x)^2 + (y)^2}
$$

Let's calculate the distance for each point:

### Point $$ A(5, 6) $$:
$$
\text{Distance}_A = \sqrt{5^2 + 6^2} = \sqrt{25 + 36} = \sqrt{61} \approx 7.81
$$

### Point $$ B(-2, 5) $$:
$$
\text{Distance}_B = \sqrt{(-2)^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39
$$

### Comparison:
- $$\sqrt{29} \approx 5.39$$ (Distance of Point B)
- $$\sqrt{61} \approx 7.81$$ (Distance of Point A)

Since $$5.39 < 7.81$$, **Point $$ B(-2, 5) $$ is closer to the origin**.

**Answer:**  
Point $$ B $$ is closer to the origin.
Point $$ B $$ is closer to the origin.