Question: Find the distance between each pair of points. Round your answer to the nearest tenth, if…

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

\[ \begin{array}{c} \text{Graph 1:} \\ \begin{array}{c|c|c|c|c|c} \hline & -4 & -2 & 0 & 2 & 4 \\ \hline -4 & & & & & \\ \hline -2 & & & & & \\ \hline 0 & & & & & \\ \hline 2 & & & & & \\ \hline 4 & & & & & \\ \hline \end{array} \end{array} \]

\[ \begin{array}{c} \text{Graph 2:} \\ \begin{array}{c|c|c|c|c|c} \hline & -4 & -2 & 0 & 2 & 4 \\ \hline -4 & & & & & \\ \hline -2 & & & & & \\ \hline 0 & & & & & \\ \hline 2 & & & & & \\ \hline 4 & & & & & \\ \hline \end{array} \end{array} \]

Solution

To find the distance between each pair of points: First Pair: (-3, 3) and (2, -1) Step 1: Identify the coordinates of the two points. \[ (x_1, y_1) = (-3, 3) & \] \[ (x_2, y_2) = (2, -1) & \] Step 2: Apply the distance formula. \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} & \] Step 3: Substitute the values into the formula. \[ d = \sqrt{(2 - (-3))^2 + (-1 - 3)^2} & \] Step 4: Calculate the differences. \[ d = \sqrt{(5)^2 + (-4)^2} & \] Step 5: Square the differences. \[ d = \sqrt{25 + 16} & \] Step 6: Sum the squares. \[ d = \sqrt{41} & \] Step 7: Calculate the square root and round to the nearest tenth. \[ d \approx 6.4 & \] Second Pair: (-3, -3) and (2, 2) Step 1: Identify the coordinates of the two points. \[ (x_1, y_1) = (-3, -3) & \] \[ (x_2, y_2) = (2, 2) & \] Step 2: Apply the distance formula. \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} & \] Step 3: Substitute the values into the formula. \[ d = \sqrt{(2 - (-3))^2 + (2 - (-3))^2} & \] Step 4: Calculate the differences. \[ d = \sqrt{(5)^2 + (5)^2} & \] Step 5: Square the differences. \[ d = \sqrt{25 + 25} & \] Step 6: Sum the squares. \[ d = \sqrt{50} & \] Step 7: Calculate the square root and round to the nearest tenth. \[ d \approx 7.1 & \]