Chapter 4.4, Problem 16PSB

To determine

To Prove: $AD\perp BC.$

Explanation of Solution

Given information: AB=AC and AD is median.

Formula used: Midpoint formula.

Proof: Take D at origin

  $\because$ D is midpoint of BC. Hence if coordinates of C are (a, 0) then of B are (-a, 0).

  

  $\because$ DA is median and AB=AC, hence A is equidistant from B and C.

  $\because$ A lees on perpendicular bisector of BC i.e. Y axis.

  $\because$ X axis and Y axis are perpendicular to each other,

  $\therefore AD\perp BC$