Question

if A(4,-6)B(3,-2)C(5,2) are vertices of triangle ABC prove that median divides the triangle in 2 equal parts.​

Answer 1

Answer:

Median: A line drawn from a vertex to it's opposite side bisecting that side is known as Median.

In every triangle median divides the opposite side into two equal lengths.

Solution:

Let us assume that Median is taken from vertex A(4, -6) to BC bisecting it at point D(x, y).

Distance between two points (x1, y1) and (x2, y2) is given by:

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

Now, Take points B( 3, -2) ; C(5,2) and find the distance between them.

You get, BC =

$\sqrt{ {(5 - 3)}^{2} + {(2 - ( - 2))}^{2} }$

=

$\sqrt{ {2}^{2} + {4}^{2} } = \sqrt{20} = 2 \sqrt{5}$

Now, BD = DC = (2√5)/2 = √5

HENCE PROVED.