Question

(Fill in the Blank)

Lamar is writing a coordinate proof to show that a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas. He starts by assigning coordinates as given.

Answer 1

The co-ordinates of N are (a,b)

an expression for the area of triangle KNM is ab.

The length of the base, ML, is 2a, and the height is b.

Hope this helps

Answer 2

Answer: 1. Coordinates of N=(a,b).

2. Area of ΔKNM=ab.

3. Base of ΔMNL= 2a and height =b.

Step-by-step explanation

1. Given: ΔKML in which N is the midpoint of L(2a,0) and and K(0,2b)

By mid point theorem the coordinates of N =
`((2a+0)/(2),(0+2b)/(2)=(a,b)`

2. Given: In ΔKNM , base MK=2b and height=a then

Area of ΔKNM=
`(1)/(2)base*\ height=(1)/(2)*2b*\ a=ab`

3.Given: Area of ΔMNL =ab

base of ΔMNL=2a ,across x axis.

Now ,

Arera of ΔMNL

`=(1)/(2)*\ base\ height=ab\\\Rightarrow(1)/(2)*\ 2a*\ height=ab\\\Rightarrow\ height=b`