student.freckle.com Login - Ga Login - Ga... Calendar $$ x y- $$ Goog... Start Page by Renaiss... Student D... NUMBER SYSTEM - 3/10 Point $$ A $$ is located at $$ (2,3) $$. Point $$ B $$ is located at $$ \left(2,-2 \frac{1}{2}\right) $$. What is the distance You can earn 5 coins $$ 4 \frac{1}{2} $$ units $$ 5 \frac{1}{2} $$ units 2 units $$ 6 \frac{1}{2} $$ units

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UpStudy AI · Accepted Answer

To find the distance between points $$ A(2, 3) $$ and $$ B\left(2, -2 \frac{1}{2}\right) $$, we can use the distance formula for two points in a Cartesian coordinate system, which is given by:

$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

### Step 1: Identify the coordinates
- Point $$ A $$ has coordinates $$ (x_1, y_1) = (2, 3) $$
- Point $$ B $$ has coordinates $$ (x_2, y_2) = \left(2, -2.5\right) $$ (since $$ -2 \frac{1}{2} = -2.5 $$)

### Step 2: Substitute the coordinates into the distance formula
Now we can substitute the coordinates into the distance formula:

$$
d = \sqrt{(2 - 2)^2 + \left(-2.5 - 3\right)^2}
$$

### Step 3: Calculate the differences
- $$ x_2 - x_1 = 2 - 2 = 0 $$
- $$ y_2 - y_1 = -2.5 - 3 = -5.5 $$

### Step 4: Substitute the differences back into the formula
Now we substitute these values back into the formula:

$$
d = \sqrt{(0)^2 + (-5.5)^2}
$$

### Step 5: Calculate the squares
- $$ (0)^2 = 0 $$
- $$ (-5.5)^2 = 30.25 $$

### Step 6: Calculate the distance
Now we can calculate the distance:

$$
d = \sqrt{0 + 30.25} = \sqrt{30.25}
$$

### Step 7: Find the square root
Calculating the square root gives us:

$$
d = 5.5
$$

### Conclusion
The distance between points $$ A $$ and $$ B $$ is $$ 5.5 $$ units.

Thus, the correct answer is $$ 5 \frac{1}{2} $$ units.
The distance between points $$ A(2, 3) $$ and $$ B\left(2, -2 \frac{1}{2}\right) $$ is $$ 5 \frac{1}{2} $$ units.

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