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(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.

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 form class=

Respuesta :

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


JeanaShupp

Answer:  1. Coordinates of N=(a,b).

2. Area of ΔKNM=ab.

3. Base of ΔMNL= 2a and height =b.

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 = [tex](\frac{2a+0}{2},\frac{0+2b}{2}=(a,b)[/tex]

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

Area of ΔKNM=[tex]\frac{1}{2}base\times\ height=\frac{1}{2}\times2b\times\ a=ab[/tex]

3.Given: Area of ΔMNL =ab

base of ΔMNL=2a ,across x axis.

Now ,

Arera of ΔMNL

[tex]=\frac{1}{2}\times\ base\ height=ab\\\Rightarrow\frac{1}{2}\times\ 2a\times\ height=ab\\\Rightarrow\ height=b[/tex]

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