Question

Find the length of the median of the triangle ABC whose vertices are A( 7 - 3 ) B( 5, 3) and C( 3, - 1) where D is midpoint of side BC

Answer 1

mid point of BC=(4,1)
AD=5units

Answer 2

Answer:

The length of median is 5 units.

Step-by-step explanation:

Given the vertices of triangle are A(7,-3), B(5,3), C(3,-1).

we have to find the length of median

As the median pass through the mid-point of the side BC i.e pass through the vertex A

Now, by mid-point formula

The coordinates of point D which is the mid-point of side BC are

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{5+3}{2},\frac{3-1}{2})=(4,1)$

By distance formula

The length of median i.e the distance between the points (7,-3) and (4,1) is

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

               $=\sqrt{(4-7)^2+(1-(-3))^2}$

               $=\sqrt{9+16}=\sqrt{25}=5units$

The length of median is 5 units.