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Chapter 2: Problem 3

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(4,-1) \text { and }(-6,3)$$

Short Answer

Expert verified
The distance between the points (4,-1) and (-6,3) is approximately 10.77 units.

Step by step solution

01

Identify the coordinates

The first point is (4,-1) so \(x_1 = 4\) and \(y_1 = -1\). The second point is (-6,3) so \(x_2 = -6\) and \(y_2 = 3\).
02

Input the values into the formula

Plug these values into the distance formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). So, it will look like \(\sqrt{(-6 - 4)^2 + (3 - -1)^2}\)
03

Simplify the expression

Simplify the expression inside the square root by first calculating the differences i.e. \(-6 - 4 = -10\) and \(3 - -1 = 4\) and then squaring these results, so it will look like \(\sqrt{(-10)^2 + 4^2}\)
04

Calculate the squares and addition

Calculate squares: \( (-10)^2 = 100\) and \(4^2 = 16\). After addition \(\sqrt{100 + 16} = \sqrt{116}\)
05

Simplify the square root and round to two decimal places

Simplify the square root. \(\sqrt{116} = 10.77\) when rounded to two decimal places.

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