Find the distance between each pair of points. Round to the nearest tenth if necessary. (-3, 6) (2,1)

Find the distance between each pair of points. Round to the nearest tenth if necessary.
(-3, 6) (2,1)

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  1. Answer:

    The distance between the two points is about 7.1 units.

    Step-by-step explanation:

    We want to find the distance between the two points (-3, 6) and (2, 1).

    To find the distance between any two points, we can use the distance formula:

    [tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

    Let (-3, 6) be (x₁, y₁) and (2, 1) be (x₂, y₂). Substitute:

    [tex]\displaystyle d=\sqrt{((2)-(-3))^2+((1)-(6))^2}[/tex]

    Simplify:

    [tex]\displaystyle d=\sqrt{(5)^2+(-5)^2}[/tex]

    Evaluate:

    [tex]d=\sqrt{25+25}=\sqrt{25(2)}=5\sqrt{2}\approx 7.1\text{ units}[/tex]

    The distance between the two points is about 7.1 units.

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