Question

I have a geometry nightmare question...If you can help...Plz do!

Answer 1

I CAN'T LOOK AT 2

Answer 2

this isn't too bad, it's just a lot of number punching once you have the idea

Answer 3

We have two main ideas here:

\(Midpoint\)
and
\(Distance \)

Answer 4

Midpoint is the the point that is exactly in the middle between two given points.

for example
does this picture make sense?

Answer 5

Midpoint of AB is
\[=((0+2a)/2,(0+0)/2)=(2a/2,0/2)=(a,0)\]
x coordinate of C is
\[=a\]
N is mid-point of AC
\[N= ((0+a)/2,(0+b)/2)=(a/2, b/2)\]
M is midpoint of BC
\[M=((2a+a)/2,(0+b)/2)=(3a/2, b/2)\]
Distance MA is
\[MA= \sqrt{(3a/2-0)^2+(b/2-0)^2} = \sqrt{(3a/2)^2+(b/2)^2} = \sqrt{9a^2/4+b^2/4}\]
Distance NB is
\[NB= \sqrt{(a/2-2a)^2+(b/2-0)^2} = \sqrt{(a/2-4a/2)^2+(b/2-0)^2}\]
\[=\sqrt{(-3a/2)^2+(b/2)^2} = \sqrt{9a^2/4+b^2/4}\]
Therefore,
MA=NB
The 2 medians are equal in an isoceles triangle.