Distance in the Coordinate Plane Quick Check

Question

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Question
Use the image to answer the question.

A straight, solid line connects plotted points E and F on a coordinate plane. The line slopes downward from left to right. Point E is left parenthesis negative 6 comma 1 right parenthesis. Point F is left parenthesis 2 comma negative 5 right parenthesis.

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

(1 point)
Responses

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=(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=((−2)+6)2+(5+1)2−−−−−−−−−−−−−−−−−−√
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−−−−−−−−−−−−−−−√

Answer 1

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

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

In this case, \((x_1, y_1) = (-6, 1)\) and \((x_2, y_2) = (2, -5)\).

Substituting these coordinates into the distance formula, we have:

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

Which simplifies to:

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

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

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

Among the options provided, the correct response would be:

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