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Problem 1031

# The point $$\mathrm{P}_{1}$$ has coordinates $$(-2,-1)$$ and the point $$\mathrm{P}_{2}$$ has coordinates $$(2,2)$$. Find the distance $\underline{P}_{1} \underline{P}_{2}$ between these points.

Expert verified
The distance between points $$\mathrm{P}_{1}$$ and $$\mathrm{P}_{2}$$ is 5 units.
See the step by step solution

## Step 1: Identify the coordinates of the points

We have the following coordinates: Point P₁: (-2, -1) Point P₂: (2, 2)

## Step 2: Apply the distance formula

We will apply the distance formula to calculate the distance between points P₁ and P₂. $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

## Step 3: Substitute the coordinates into the formula

Now, we substitute the coordinates of P₁ and P₂ into the distance formula: $$d = \sqrt{[(2 - (-2))^2 + (2 - (-1))^2]}$$

## Step 4: Simplify the expression

Now, let's simplify the expression by performing the operations within the parentheses: $$d = \sqrt{[(2 + 2)^2 + (2 + 1)^2]}$$

## Step 5: Perform the operations

We can now perform the operations within the parentheses: $$d = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9}$$

## Step 6: Final calculation

Finally, we can add the numbers within the square root and find the square root of the result: $$d = \sqrt{25} = 5$$ Therefore, the distance between points $$\mathrm{P}_{1}$$ and $$\mathrm{P}_{2}$$ is 5 units.

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