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A line segment has endpoints (-7,3) and (-19,-6). What is the length of the segment? (A) 3sqrt7 units (B) 3sqrt17 units (C) 15 units (D) 10sqrt2 units

3333. A line segment has endpoints (−7,3) (-7,3) and (−19,−6) (-19,-6) . What is the length of the segment?\newline(A) 37 3 \sqrt{7} units\newline(B) 317 3 \sqrt{17} units\newline(C) 1515 units\newline(D) 102 10 \sqrt{2} units

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Full solution

Q. 3333. A line segment has endpoints (−7,3) (-7,3) and (−19,−6) (-19,-6) . What is the length of the segment?\newline(A) 37 3 \sqrt{7} units\newline(B) 317 3 \sqrt{17} units\newline(C) 1515 units\newline(D) 102 10 \sqrt{2} units
  1. Calculate Differences: Calculate the differences in the xx-coordinates and yy-coordinates of the endpoints.\newlineDifference in xx-coordinates: −7−(−19)=12-7 - (-19) = 12\newlineDifference in yy-coordinates: 3−(−6)=93 - (-6) = 9
  2. Use Distance Formula: Use the distance formula to find the length of the segment: (x2−x1)2+(y2−y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. Substitute the differences calculated: (12)2+(9)2=144+81=225\sqrt{(12)^2 + (9)^2} = \sqrt{144 + 81} = \sqrt{225}
  3. Simplify Square Root: Simplify the square root to find the final distance. 225=15\sqrt{225} = 15

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