Question

A(5, 1), B(1, 5) and C(-3, -1) are the vertices ∆ ABC . Find the length of median AD

Answer 1

Answer:

4,1 is the answer is it right or wrong

Answer 2

$\huge\frak\red{AnSwer}$

as we know median through a divides the line bc in two equal halves .

so , co-ordinates of d will be :

let its co-ordinates be ( x , y )

Given :-

X1 = 1 , y1 = 5 , X2 = 3 , y2 = 1 , through mid-point formula .

• for x co-ordinate

$x = \frac{(x1 + x2}{2}$

$x = \frac{1 + 3}{2}$

$x = \frac{4}{2}$

$x = 2$

• for y co-ordinate

$y = \frac{(y1 + y2}{2}$

$y = \frac{(5 + 1}{2}$

$y = \frac{6}{2}$

$y = 3$

now the co-ordinates of d are ( 2,3 ) now through distance formula X1=5 , y1 = 1 , X2= 2 , y2 = 3 .

$ad \times 2 = (x2 - x1) \times 2 + \\ (y2 - y1) \times 2$

$ad \times 2 = ( - 3) \times 2 + (2) \times 2$

$dd \times 2 = 9 + 4$

taking square root both sides

We get ,

$ad \times 2 = 13$

$therefore \: ad = 6.5units$