If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is

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KollegeApply · Accepted Answer

It is given that A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC. Let CD be the median of ∆ABC through C. Then, D is the mid-point of AB. Using mid-point formula, we get Coordinates of D = \left( 4 + $\frac{2}{2}$, 9 + $\frac{3}{2}$ \right) = \left( $\frac{6}{2}$, $\frac{12}{2}$ \right) = \left( 3, 6 \right) $\therefore$ Length of the median, AD = \sqrt{\left( 6 - 3 \right)^2 + \left( 5 - 6 \right)^2} \left( \text{ Using distance formula } \right) = \sqrt{3^2 + \left( - 1 \right)^2} = $\sqrt$(10) \text{ units } Thus, the length of the required median is $\sqrt$(10) units. [Solution diagram: 64156_solution_1.png]

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