1. ## Analytic geometry

1. A triangle has vertices D(1,3), E(-3, 2) and F (-2, -2)
a)Classify the triangle by side length (i.e equalateral, isosceles or scalene).

b) Determine the perimeter of the triangle, to the nearest tenth.

2. Determine the equation of the following circles with centre ( 0,0) and the given radius.

b) r = 10

c) r = sq root 3

Can anyone help me please? With all the work to get the answers too?

I would really appreciate it.

2. 1. Find the lengths of each side of the triangle using the distance formula: $\displaystyle d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$ where $\displaystyle (x_{1}, y_{1})$ and $\displaystyle (x_{2}, y_{2})$ represents your two points. How many of the lengths are equal?

2. Equation of a circle is given by: $\displaystyle (x - a)^{2} + (y - b)^{2} = r^{2}$ where (a, b) is your centre of the circle and r (not squared) is your radius. Just simply plug in your values.

3. I don't understand?
Can you elaborate a bit more? Like give the answers step by step?

Here's my hw page if you need.

4. What don't you understand? On the xy coordinate system, plot the points to get a general idea of what the triangle looks like. Then find the lengths of DE, EF, and DF using the distance formula as posted earlier. For example, the distance from D(1, 3) to E(-2, -2) is found by:
$\displaystyle d = \sqrt{(1 - (-2))^{2} + (3 - (-2))^{2}} = \sqrt{34}$

Similarly, find the other lengths of the triangle and compare them. You know that equilateral triangles have equal sides, isoceles triangles have 2 equal sides, and scalene triangles have no equal sides.

For the questions involving the circle, you did it for r = 3. It's not any different using r = 10 and r = $\displaystyle \sqrt{3}$.

5. Originally Posted by o_O
What don't you understand? On the xy coordinate system, plot the points to get a general idea of what the triangle looks like. Then find the lengths of DE, EF, and DF using the distance formula as posted earlier. For example, the distance from D(1, 3) to E(-2, -2) is found by:
$\displaystyle d = \sqrt{(1 - (-2))^{2} + (3 - (-2))^{2}} = \sqrt{34}$

Similarly, find the other lengths of the triangle and compare them. You know that equilateral triangles have equal sides, isoceles triangles have 2 equal sides, and scalene triangles have no equal sides.

For the questions involving the circle, you did it for r = 3. It's not any different using r = 10 and r = $\displaystyle \sqrt{3}$.
Oh, okay i get question one now, thanks

for for question 2, dertermining the radius question a) my friend did it for me, but can you step by step me through $\displaystyle b)$$\displaystyle r = 10$, then i can do $\displaystyle c) r = \sqrt{3}$on my own?

6. On your sheet, I can see you did it for r = 3. The procedure is no different from using r = 10.

7. Originally Posted by o_O
On your sheet, I can see you did it for r = 3. The procedure is no different from using r = 10.
I have no idea how to do it, like i said my friend did it for me.
But im confused here though,

r=3
x squared + 4 squared = r squared
x squared + 4 squared = 3 squared
x squared + 4 squared = 9

Sorry about the "squared" i don't know how to use the function squared.

Anyways where does this 4 come from?

8. ... That's a y, not a 4 ...

Did you read what I posted earlier? The equation of a circle is given by: $\displaystyle (x - a)^{2} + (y - b)^{2} = r^{2}$ where (a,b) represents the centre of your circle and r (not squared) represents your radius.

For your question, you are given (a,b) (which is (0,0) ) and you are given r = 3. So simply plug it into the equation above:
$\displaystyle (x - 0)^{2} + (y - 0)^{2} = (3)^{2}$
$\displaystyle x^{2} + y^{2} = 9$

That's all you can do.

9. Originally Posted by o_O
... That's a y, not a 4 ...

Did you read what I posted earlier? The equation of a circle is given by: $\displaystyle (x - a)^{2} + (y - b)^{2} = r^{2}$ where (a,b) represents the centre of your circle and r (not squared) represents your radius.

For your question, you are given (a,b) (which is (0,0) ) and you are given r = 3. So simply plug it into the equation above:
$\displaystyle (x - 0)^{2} + (y - 0)^{2} = (3)^{2}$
$\displaystyle x^{2} + y^{2} = 9$

That's all you can do.
Ooh, im sorry! Lmao i misread it.
Now i understand everything. Thanks! i really appreciate it