(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.

 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 =

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

Area of ΔKNM=

3.Given: Area of ΔMNL =ab

base of ΔMNL=2a ,across x axis.

Now ,

Arera of ΔMNL

12/60 students chose science fiction

Approximately x/150 students prefer sf

60x = 1800

x = 30

30/150 students are assumed to prefer sf

30/150 = x/100

150x = 3000

x = 20

20/100 students are likely to prefer sf

Mr. Rodriguez made a reasonable estimate for the approximate percentage of students that prefer science fiction, because if 12/60 is equivalent to 30/150 which refers to the number of students who can be assumed to prefer science Fiction out of the whole school. Considering we need to identify what 30/150 as a percentage is, we can reduce it down to 1/5 to make I easier, then divide 1 by 5 to get .2
.2 as a percentage is 20%, so his inference was indeed reasonable.

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