Hey guys! I'm

Tim-Math-y your scribe today..

Today, we started off class with our usual MENTAL MATH. Moving that aside, we reviewed last night's homework which I believe was Exercise #22.

Now today's lesson was

**Proving Assertions Using Coordinate Geometry **which was on a handout.With this lesson, "our goal is to

**USE** and

**MANIPULATE** (control) the formulas any way we can in order to prove certain assertions and/or theorems in coordinate geometry (about shapes on a graph)".

With the first example, Given A=(-1,3), B=(0,5), and C=(-2,6)

a.) Verify that ABC is a right triangleWe start by drawing a diagram which should be something like..

Now with that, we find the lengths of the triangle so that we can

**prove** that this triangle is a right triangle with the

**Pythagorean Theorem**.

Using the distance formulas d=root(x1-x2)

^{2}+(y1-y2)

^{2}, we find that distance AB=root(5), distance BC=root(5) and distance AC=root(10). With these values, we plus them into the pythagorean theorem which is a

^{2} + b

^{2} = c

^{2}.

root(5)^{2} + root(5)^{2} = root(10)^{2}

5 + 5 = 10

10 = 10

This means that the triangle is indeed a Right Triangle.

b.) Is ABC isosceles? justify your assertionThis should be a simple answer like this:

Yes, because AB=BC. :)

c.) If M is the midpoint of AB and B is the midpoint of AC, prove that MN is parallel to BC.Start by drawing a simple diagram.With this, we first must find the coordinates of N and M by finding the midpoints of AC and AB. We do this by utilizing the formula:

mpt=(x1+x2/2 , y1+y2/2)We find that the coordinates are N(-3/2 , 9/2) and M(-1/2 , 4).. yess eeew to fractions.

With that, we now prove that the two lines are parallel by finding both of their slopes. We do this by using the formula:

M(slope)=(y1-y)/(x1-x)

To cut this short, the two slopes are equal values which were -1/2. With that we conclude that they are parallel with a statement:

M_{MN} = M_{BC} therefore, MN is parallel to BC

Now comes the hard questions which I must apologize because my brother must use the computer for his own homework purposes thus booting me off :( .

Homework for today is Ex.#23 i think.

There is also a Quiz this friday.

TOMORROW's SCRIBE IS .... hmm.. I'm looking on the scribe list and I know mr. Jojo was scribe yesterday so... the list must be old but I pick the next one in line who is..... JAMILYN G.!

Have a great.. rest of day. lol