Question

MATH QUESTION!! WILL MARK BRAINLIEST!! PAST DUE HELP ASAP!!!

Answer 1

Answer:

Proof below

Step-by-step explanation:

Right Triangles

In any right triangle, i.e., where one of its internal angles is 90°, some interesting relations stand. One of the most-used is Pythagora's Theorem.

In a right triangle with shorter sides a and b, and longest side c, called the hypotenuse, the following equation is satisfied:

$c^2=a^2+b^2$

The image provided in the question shows a line passing through points A(0,4) and B(3,0) that forms a right triangle with both axes.

The origin is marked as C(0,0) and the point M is the midpoint of the segment AB. We have to prove.

$CM=\frac{1}{2}AB$

First, find the coordinates of the midpoint M(xm,ym):

$\displaystyle x_m=\frac{0+3}{2}=1.5$

$\displaystyle y_m=\frac{4+0}{2}=2$

Thus, the midpoint is M( 1.5 , 2 )

Calculate the distance CM:

$CM=\sqrt{(1.5-0)^2+(2-0)^2}$

$CM=\sqrt{2.25+4}=\sqrt{6.25}=2.5$

CM=2.5

Now find the distance AB:

$AB=\sqrt{(3-0)^2+(4-0)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}$

AB=5

AB/2=2.5

It's proven CM is half of AB