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Find the distance between the points (10,9)(10,9) and (−2,−7)(-2,-7).\newlineR Round decimals to the nearest tenth. ___\_\_\_ units

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Full solution

Q. Find the distance between the points (10,9)(10,9) and (−2,−7)(-2,-7).\newlineR Round decimals to the nearest tenth. ___\_\_\_ units
  1. Calculate Differences: Calculate the differences in the xx-coordinates and yy-coordinates of the points.\newlineDifference in xx-coordinates: 10−(−2)=1210 - (-2) = 12\newlineDifference in yy-coordinates: 9−(−7)=169 - (-7) = 16
  2. Use Distance Formula: Use the distance formula: Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. Substitute the differences: Distance=122+162=144+256=400\text{Distance} = \sqrt{12^2 + 16^2} = \sqrt{144 + 256} = \sqrt{400}
  3. Calculate Square Root: Calculate the square root of 400400 to find the distance.\newline400=20\sqrt{400} = 20

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