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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=((−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−−−−−−−−−−−−−−−√
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−−−−−−−−−−−−−−−√
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

Answer 1

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

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

Where $(x_1,y_1)$ are the coordinates of point E and $(x_2,y_2)$ are the coordinates of point F. Substituting in the specific coordinates:

• $x_1=-6$, $y_1=1$
• $x_2=2$, $y_2=-5$

The distance formula setup would be:

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

This simplifies to:

$$d=\sqrt{(2+6{)}^2+(-5-1{)}^2}$$ $$d=\sqrt{(8{)}^2+(-6{)}^2}$$

None of the provided responses are exactly correct because they contain errors in the setup. However, the closest response, employing the correct adjustments, would be:

d = square root of open paren 2 minus negative 6 close paren squared plus open paren negative 5 minus 1 close paren squared end root

Since the intended expression and calculations involve:

• $x_2-x_1=2-(-6)=2+6=8$
• $y_2-y_1=-5-1=-6$

To sum it all up, the official option setup was not available, but the closely matching answer with positioning correction should be indicated.