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Chapter 32: Chapter 32

Problem 1031

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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.

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The distance between points \(\mathrm{P}_{1}\) and \(\mathrm{P}_{2}\) is 5 units.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

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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