Question

a maths ques solve it....plzz.. fast ----------<br /><br />class 11 maths straight lines.... .

* using concept of slope prove that medians of an equilateral triangle are perpendicular to the corresponding sides *

Answer 1

 
 


 

It is given that DABC is an equilateral triangle, therefore

AB = AC = BC = 2a

Now,

AB = AC

⇒AB2 = AC2

⇒ (a + a)2 + (b – 0)2 = (α – a)2 + (b – 0)2

⇒ 4aα = 0

⇒ α = 0

On applying Pythagoras theorem in right triangle COA, we have



Thus, we get the coordinates of A as and point A lies on Y-axis, therefore

 OA ⊥ BC  OA is along Y-axis and BC is along X-axis]

Let D and E be the mid-points of AC and AB respectively. Then, the coordinates of D and E will berespectively.



Similarly,



∴AB ⊥ CE

Thus, AO, BD and CE are medians of the equilateral triangle ABC in such a way that AO ⊥ BC, BD ⊥ AC and CE ⊥ AB.

Hence, medians of an equilateral triangle are perpendicular to the corresponding sides.