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Find the distance between the points (1,−3)(1,-3) and (6,−8)(6,-8). If necessary, round your answer to the nearest tenth. ___\_\_\_ units

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Q. Find the distance between the points (1,−3)(1,-3) and (6,−8)(6,-8). If necessary, round your answer to the nearest tenth. ___\_\_\_ units
  1. Identify Coordinates and Formula: Step 11: Identify the coordinates of the points and the formula to use.\newlineWe have points (1,−3)(1, -3) and (6,−8)(6, -8). The distance formula is (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. Substitute into Formula: Step 22: Substitute the coordinates into the distance formula.\newlineCalculate x2−x1x_2 - x_1 and y2−y1y_2 - y_1.\newlinex2−x1=6−1=5x_2 - x_1 = 6 - 1 = 5\newliney2−y1=−8−(−3)=−5y_2 - y_1 = -8 - (-3) = -5
  3. Square the Differences: Step 33: Square the differences.\newline(x2−x1)2=52=25(x_2 - x_1)^2 = 5^2 = 25\newline(y2−y1)2=−52=25(y_2 - y_1)^2 = -5^2 = 25
  4. Add and Take Square Root: Step 44: Add the squares and take the square root. (x2−x1)2+(y2−y1)2=25+25=50\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{25 + 25} = \sqrt{50}
  5. Simplify Square Root: Step 55: Simplify the square root. 50=5×2\sqrt{50} = 5 \times \sqrt{2}

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