Question

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

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

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

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

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

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify the coordinates

Let \((x_1,y_1)=(9,-2)\) and \((x_2,y_2)=(6,3)\).

Step3: Substitute into the formula

Substitute \(x_1 = 9,y_1=-2,x_2 = 6,y_2 = 3\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
We get \(d=\sqrt{(6 - 9)^2+(3-(-2))^2}\).

Answer:

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