Question

A(5, 1); b(1, 5) and c(3, 1) are the vertices of abc. Find the length of median ad.

Answer 1

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

so , coordinates of d will be:

let its coordinates be (x,y)

given:- x1=1 , y1=5 , x2=3 , y2=1;

through mid point formula:

• for x coordinate

x = (x1 + x2 )/ 2

x = (1+3)/2

x = 4/2

x = 2

• for y coordinate :

y = (y1 + y2)/2

y = (5+1)/2

y = 6/2

y = 3

now the coordinates of d are (2,3)

now through distance formula :-

x1 = 5 , y1 = 1 , x2 = 2 , y2 = 3

ad^2 = (x2 - x1)^2 + (y2 - y1)^2

ad^2 = (-3)^2 +(2)^2

ad^2 = 9 + 4

taking square root both sides

we get : ad = _/ 13 units

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