Answered

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Find the distance between the two points.
(2,2)

(-3,-4)
Enter the number that
goes beneath the
radical symbol. ✓ [?]

Sagot :

amysun2025

Answer:

[tex]\sqrt{61}[/tex]

Step-by-step explanation:

Hi there!

We are given the points (2, 2) and (-3, -4).

We want to find the distance between them.

We can use the distance formula for that, which 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 points

We have two points, which is needed for that, but let's label their values to avoid confusion

[tex]x_1=2\\y_1=2\\x_2=-3\\y_2=-4[/tex]

Now substitute those values into the formula to find the distance

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

[tex]\sqrt{(-3-2)^2+(-4-2)^2}[/tex]

Simplify the values under the radical

[tex]\sqrt{(-5)^2+(-6)^2}[/tex]

Raise the numbers under the radical

[tex]\sqrt{25+36}[/tex]

Add the numbers under the radical together

[tex]\sqrt{61}[/tex]

The answer cannot be simplified down further, so [tex]\sqrt{61}[/tex] is the answer.

Hope this helps!

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