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Which equation correctly shows how to determine the distance between the points (9, –2) and (6, 3) on a coordinate grid?

Which equation correctly shows how to determine the distance between the points 9 2 and 6 3 on a coordinate grid class=

Respuesta :

luisejr77

Answer: [tex]d=\sqrt{(6-9)^2+(3-(-2))^2}[/tex] (Third option)

Step-by-step explanation:

The formula for calculate the distance (d) between two points is:

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

Given the points (9,-12) and (6,3), you can identify:

[tex]x_2=6\\x_1=9\\y_2=3\\y_1=-2[/tex]

Substitute these coordinates into the formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] to find the equation that  correctly shows how to determine the distance between the given points (9,-12) and (6,3).

Then:

[tex]d=\sqrt{(6-9)^2+(3-(-2))^2}[/tex] (Third option)

kudzordzifrancis

ANSWER

[tex]d = \sqrt{ {(6 - 9)}^{2} + {(3 - ( - 2))}^{2} } [/tex]

EXPLANATION

To find the distance between any two points

[tex](x_1,y_1)[/tex]

and

[tex](x_2,y_2)[/tex]

We use the distance formula;

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

We let

[tex](x_1,y_1) = (9, - 2)[/tex]

and

[tex](x_2,y_2) = (6, 3)[/tex]

We substitute the coordinates into the formula to get;

[tex]d = \sqrt{ {(6 - 9)}^{2} + {(3 - ( - 2))}^{2} } [/tex]

The third choice is correct.

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