Question

How would you set up the distance formula to find the distance between points E and F . (1 point) Responses d=(2−6)2+(5−1)2−−−−−−−−−−−−−−−√ 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=(−6−2)2+(1−(−5))2−−−−−−−−−−−−−−−−−−−√ 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=(6−2)2+(1−5)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 6 minus 2 close paren squared plus open paren 1 minus 5 close paren squared end root d=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√

Answer 1

To find the distance between two points \( E(x_1, y_1) \) and \( F(x_2, y_2) \) in the Cartesian plane, you can use the distance formula:

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

Given that there are multiple responses presented, let's assume you want to set up an example with two points. Let’s denote point E as \( (x_1, y_1) \) and point F as \( (x_2, y_2) \).

If we take an example where \( E(2, 5) \) and \( F(6, 1) \), you would set up the distance formula as below:

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

Breaking this down:

- The calculation for the x-coordinates would be \( (6 - 2) = 4 \), so we square it: \( (4)^2 = 16 \).
- The calculation for the y-coordinates would be \( (1 - 5) = -4 \), so we square it: \( (-4)^2 = 16 \).

Then substituting back into the distance formula:

\[
d = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}
\]

Now, from the options you provided, the correct setup of the distance formula would be:

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

This matches closely with option 3 from your responses.

Answer 2

DaQuan marks two points on the coordinate plane. One point is L(4,2) and the other point is M(7,6) . What is the correct way for DaQuan to set up the distance formula?(1 point) Responses d=(4−7)2+(2−6)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 4 minus 7 close paren squared plus open paren 2 minus 6 close paren squared end root d=(2−4)2+(6−7)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 2 minus 4 close paren squared plus open paren 6 minus 7 close paren squared end root d=(2−7)2+(4−6)2−−−−−−−−−−−−−−−√ d is equal to square root of open paren 2 minus 7 close paren squared plus open paren 4 minus 6 close paren squared end root d=(6−7)2+(2−4)2−−−−−−−−−−−−−−−√

Answer 3

To set up the distance formula correctly for the points \( L(4, 2) \) and \( M(7, 6) \), you'll use the formula:

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

In this case:
- Point \( L \) has coordinates \( (x_1, y_1) = (4, 2) \)
- Point \( M \) has coordinates \( (x_2, y_2) = (7, 6) \)

Substituting these values into the formula gives:

\[
d = \sqrt{(7 - 4)^2 + (6 - 2)^2}
\]

Calculating the differences:
- For the x-coordinates: \( 7 - 4 = 3 \)
- For the y-coordinates: \( 6 - 2 = 4 \)

Thus, the correct setup will be:

\[
d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

Looking at the responses you provided, the setup that reflects this calculation is:

\[
d = \sqrt{(4 - 7)^2 + (2 - 6)^2}
\]

This option is equivalent to the correct one because it results in the same squared differences:

\[
d = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16}
\]

So the answer is:

**\( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \)**