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Chapter 0: Problem 13

Find the distance between the given pairs of points. $$ (1,-1) \text { and }(2,-2) $$

Short Answer

Expert verified
The distance between the points (1, -1) and (2, -2) is \(\sqrt{2}\).

Step by step solution

01

Identify the coordinates of the two points

Let's denote the two points as point A and point B. From the given information, we have: Point A (x1, y1) = (1, -1) Point B (x2, y2) = (2, -2)
02

Apply the distance formula

Now, we will apply the distance formula using the coordinates of points A and B: Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
03

Substitute the values

Substituting the values of coordinates from Step 1 into the formula, we get: Distance = \(\sqrt{(2 - 1)^2 + (-2 - (-1))^2}\)
04

Simplify the expression

Now we can simplify the expression inside the square root: Distance = \(\sqrt{(1)^2 + (-1)^2}\)
05

Solve

Finally, we calculate the square root of the sum: Distance = \(\sqrt{1 + 1}\) Distance = \(\sqrt{2}\)
06

Write the final answer

The distance between the points (1, -1) and (2, -2) is \(\sqrt{2}\).

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