Respuesta :

Ben

[tex]\huge{\boxed{2 \sqrt{101}}}[/tex]

The distance formula is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.

Substitute in the points. [tex]\sqrt{(2-4)^2+(-8-12)^2}[/tex]

Subtract. [tex]\sqrt{(-2)^2+(-20)^2}[/tex]

Solve the exponents. [tex]\sqrt{4+400}[/tex]

Add. [tex]\sqrt{404}[/tex]

Now, we can simplify this square root just a little bit. [tex]404[/tex] has a square factor of [tex]4[/tex]. [tex]\sqrt{404}=\sqrt{4}*\sqrt{101}[/tex]

The square root of [tex]4[/tex] equals [tex]2[/tex]. [tex]\boxed{2 \sqrt{101}}[/tex]

luisejr77

Answer: [tex]2\sqrt{101}[/tex]

Step-by-step explanation:

The distance between two points can be calculated with the following formula:

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

Given the points  P(12, 4) and Q(-8, 2), we can identify that:

[tex]x_2=-8\\x_1=12\\y_2=2\\y_1=4[/tex]

Then, substituing values into the formula, we get that the distance between these two points is:

[tex]d_{(PQ)}=\sqrt{(-8-12)^2+(2-4)^2}\\\\d_{(PQ)}=2\sqrt{101}[/tex]

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