Find the distance between the points (2,8) and (8,8). ____ units

Identify Coordinates and Formula: Step 1: Identify the coordinates of the points and the formula to use. We have points (2,8) and (8,8). To find the distance between two points in a coordinate plane, we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]Substitute into Distance Formula: Step 2: Substitute the coordinates into the distance formula. Here, $x_1 = 2$, $y_1 = 8$, $x_2 = 8$, and $y_2 = 8$. Plugging these into the formula gives: \[ \text{Distance} = \sqrt{(8 - 2)^2 + (8 - 8)^2} \]Simplify the Expression: Step 3: Simplify the expression. Calculate inside the square root: \[ (8 - 2)^2 = 6^2 = 36 \] \[ (8 - 8)^2 = 0^2 = 0 \] So, the distance is: \[ \text{Distance} = \sqrt{36 + 0} = \sqrt{36} \]Final Square Root Calculation: Step 4: Final calculation of the square root. \[ \sqrt{36} = 6 \] So, the distance between the points is 6 units.

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Find the distance between the points $(2,8)$ and $(8,8)$ . $\newline$ ____ units

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Q. Find the distance between the points

(2,8)

and

(8,8)

\newline

____ units

Identify Coordinates and Formula: Step $1$ : Identify the coordinates of the points and the formula to use. $\newline$ We have points ( $2$ , $8$ ) and ( $8$ , $8$ ). To find the distance between two points in a coordinate plane, we use the distance formula: $\newline$ $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute into Distance Formula: Step $2$ : Substitute the coordinates into the distance formula. $\newline$ Here, $x_1 = 2$ , $y_1 = 8$ , $x_2 = 8$ , and $y_2 = 8$ . Plugging these into the formula gives: $\newline$ $\text{Distance} = \sqrt{(8 - 2)^2 + (8 - 8)^2}$
Simplify the Expression: Step $3$ : Simplify the expression. $\newline$ Calculate inside the square root: $\newline$ $(8 - 2)^2 = 6^2 = 36$ $\newline$ $(8 - 8)^2 = 0^2 = 0$ $\newline$ So, the distance is: $\newline$ $\text{Distance} = \sqrt{36 + 0} = \sqrt{36}$
Final Square Root Calculation: Step $4$ : Final calculation of the square root. $\newline$ $\sqrt{36} = 6$ $\newline$ So, the distance between the points is $6$ units.