Question

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) \(\sqrt {\frac {13}{2}}\) units

This question was posed to me at a job interview.

This key question is from Geometry topic in chapter Coordinate Geometry of Mathematics – Class 10

Answer 1

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