Question

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

Answer 1

Answer: $d=\sqrt{(6-9)^2+(3-(-2))^2}$ (Third option)

Step-by-step explanation:

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

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

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

$x_2=6\\x_1=9\\y_2=3\\y_1=-2$

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

Then:

$d=\sqrt{(6-9)^2+(3-(-2))^2}$ (Third option)

Answer 2

ANSWER

$d = \sqrt{ {(6 - 9)}^{2} + {(3 - ( - 2))}^{2} }$

EXPLANATION

To find the distance between any two points

$(x_1,y_1)$

and

$(x_2,y_2)$

We use the distance formula;

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

We let

$(x_1,y_1) = (9, - 2)$

and

$(x_2,y_2) = (6, 3)$

We substitute the coordinates into the formula to get;

$d = \sqrt{ {(6 - 9)}^{2} + {(3 - ( - 2))}^{2} }$

The third choice is correct.