How would you set up the distance formula to find the distance between points E

Question

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and F
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(1 point)
Responses

d=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√
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6
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d is equal to square root of open paren negative 6 minus 2 close paren squared plus open paren 1 minus negative 5 close paren squared end root

d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√
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2
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6
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d is equal to square root of open paren 2 minus 6 close paren squared plus open paren 5 minus 1 close paren squared end root

d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
𝑑
=
(
(
−
2
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+
6
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2
+
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5
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1
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d is equal to square root of open paren negative 2 plus 6 close paren squared plus open paren 5 plus 1 close paren squared end root

d=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√

E (-6,1) and F (2,-5)

Answer 1

To find the distance between points \( E(-6, 1) \) and \( F(2, -5) \) using the distance formula, you will use the formula:

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

Where:

• \( (x_1, y_1) \) are the coordinates of point E (-6, 1).
• \( (x_2, y_2) \) are the coordinates of point F (2, -5).

Plugging in the values:

• \( x_1 = -6 \), \( y_1 = 1 \)
• \( x_2 = 2 \), \( y_2 = -5 \)

Now, substituting these values into the formula gives:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]

This simplifies to:

\[ d = \sqrt{(2 + 6)^2 + (-5 - 1)^2} \] \[ d = \sqrt{(8)^2 + (-6)^2} \] \[ d = \sqrt{64 + 36} \] \[ d = \sqrt{100} \] \[ d = 10 \]

So, the correct setup for the distance formula for these points \( E \) and \( F \) is:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]

From the provided options, the correct expression that matches this calculation is:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]

which simplifies down as shown above. None of the provided options match exactly, but this is how the calculation should be set up.

Answer 2

whats the best option tho

Answer 3

Given the coordinates of points \( E(-6, 1) \) and \( F(2, -5) \), the distance formula is most appropriately set up as follows:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \]

Upon looking at the provided options:

1. Option 1: \( d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \)
2. Option 2: \( d = \sqrt{(2 - 6)^2 + (5 - 1)^2} \)
3. Option 3: \( d = \sqrt{((-2) + 6)^2 + (5 + 1)^2} \)
4. Option 4: \( d = \sqrt{(6 - 2)^2 + (1 - 5)^2} \)

The best option is:

Option 1:

\[ d = \sqrt{(-6 - 2)^2 + (1 - (-5))^2} \]

Although it has negative values in both parts, it correctly reflects the calculation needed to find the distance.

However, to clarify, the correct form for the points you provided should look like this, as I mentioned earlier:

\[ d = \sqrt{(2 - (-6))^2 + (-5 - 1)^2} \quad \text{(which is equivalent to the valid calculation indicated)} \]

But between the options provided, Option 1 is the most appropriate for the points \( E \) and \( F \).