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Chapter 0: Problem 16

Find the distance between the given pairs of points. $$ (a, a) \text { and }(b, b) $$

Short Answer

Expert verified
The distance between the given pairs of points \((a, a)\) and \((b, b)\) is \(d = \sqrt{2(b - a)^2}\).

Step by step solution

01

Identify the coordinates of the points

The coordinates of the first point, \((a, a)\), are \(x_1 = a\) and \(y_1 = a\). Likewise, the coordinates of the second point, \((b, b)\), are \(x_2 = b\) and \(y_2 = b\).
02

Apply the distance formula

Using the distance formula with the given coordinates, we can find the distance between the two points as follows: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(b - a)^2 + (b - a)^2} \]
03

Simplify the expression

Now, we can simplify the expression under the square root: \[ \sqrt{(b - a)^2 + (b - a)^2} = \sqrt{2(b - a)^2} \]
04

Final answer

The distance between the given pairs of points is: \[ d = \sqrt{2(b - a)^2} \]

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