Question

If two vertices join the hypotenuse of the right angle triangle are (0,0) and (3,4) then the length of the median through the vertices have right angle is

Answer 1

5/2 be the require length

Answer 2

Answer:

Length of median through the vertices have right angle is 2.5.

Explanation:

Two vertices join the hypotenuse of the right angle triangle are O(0,0) and A(3,4) as shown in attachment.

We need to find the length of median through the vertices of right angle at B.

Distance of median = d

First we find the mid point of OA

$\text{Mid-point of O and A: }=(\frac{3}{2},2)$

Coordinate of vertices of right angle at B is (3,0)

Now we find the distance d between two points M and B using distance formula.

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

$\therefore d=\sqrt{(1.5-3)^2+(2-0)^2}\Rightarrow \sqrt{2.25+4}\Rightarrow \sqrt{6.25}=2.5$

Thus, Length of median through the vertices have right angle is 2.5.