Homework \#12 Distance on a Coordinate Grid $$ \begin{array}{l} ext { 2. Find the distance } \ ext { between the points } \ (3,5) ext { and }(6,5)\end{array} $$

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Homework \#12 Distance on a Coordinate Grid $$ \begin{array}{l}	ext { 2. Find the distance } \ 	ext { between the points } \ (3,5) 	ext { and }(6,5)\end{array} $$

UpStudy AI · Accepted Answer

To find the distance between the two points $$(3, 5)$$ and $$(6, 5)$$ on a coordinate grid, you can use the **distance formula**. However, in this case, since both points share the same $$y$$-coordinate, the problem simplifies considerably. Here's a step-by-step explanation:

### Step 1: Identify the Coordinates
- **Point A:** $$(3, 5)$$
- **Point B:** $$(6, 5)$$

### Step 2: Understand the Position
- Both points have the same $$y$$-coordinate ($$5$$), which means they lie on a **horizontal line**.

### Step 3: Use the Distance Formula
The general distance formula between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Plugging in the values:
$$
\text{Distance} = \sqrt{(6 - 3)^2 + (5 - 5)^2}
$$
$$
\text{Distance} = \sqrt{(3)^2 + (0)^2}
$$
$$
\text{Distance} = \sqrt{9 + 0}
$$
$$
\text{Distance} = \sqrt{9}
$$
$$
\text{Distance} = 3
$$

### Step 4: Conclusion
The distance between the points $$(3, 5)$$ and $$(6, 5)$$ is **3 units**.

---

**Visualization:**

Since both points are on the same horizontal line ($$y = 5$$), the distance is simply the difference in their $$x$$-coordinates.

```
Point A: (3,5) --------- Point B: (6,5)
```

The number of units between $$3$$ and $$6$$ on the $$x$$-axis is $$3$$ units.
The distance between the points $$(3, 5)$$ and $$(6, 5)$$ is **3 units**.

Homework \#12 Distance on a Coordinate Grid \( \begin{array}{l}\text { 2. Find the distance } \\ \text { between the points } \\ (3,5) \text { and }(6,5)\end{array} \)

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