InterviewSolution
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InterviewSolution
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What will be the length of the median through the vertex A, if the coordinates of the vertices of∆ABC are A(2, 5), B(5, 0), C(-2, 5)?(a) \(\sqrt {\frac {113}{3}}\) units(b) \(\sqrt {\frac {13}{2}}\) units(c) \(\sqrt {\frac {113}{2}}\) units(d) \(\sqrt {\frac {13}{2}}\) unitsThis question was posed to me at a job interview.This key question is from Geometry topic in chapter Coordinate Geometry of Mathematics – Class 10 |
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Answer» CORRECT choice is (B) \(\SQRT {\frac {13}{2}}\) units Best explanation: The median through A will BISECT the line BC. Hence, D is the midpoint of BC Coordinates of D = \((\frac {x_1+x_2}{2}, \frac {y_1+y_2}{2} ) = ( \frac {5-2}{2}, \frac {0-5}{2} ) =( \frac {3}{2}, \frac {-5}{2} )\) Distance between A and D = \( \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2} \) = \( \sqrt {(2-\frac {3}{2})^2+ (5+\frac {5}{2})^2} \) = \( \sqrt {(\frac {1}{2})^2+ (\frac {15}{2})^2} \) = \( \sqrt {\frac {1}{4}+ \frac {225}{4}} \) = \( \sqrt {\frac {113}{2}} \) units |
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