1. ## coordinates

A(1,3) and B(2,6) are points on a coordinate plane.

(a)Find the lenght of OA,OB,AB where O is the origin.
(b)Show that the points O,A,B lie on a straight line.
(c) What is the relationship between point A and the line of segment?

2. Originally Posted by helloying
A(1,3) and B(2,6) are points on a coordinate plane.

(a)Find the lenght of OA,OB,AB where O is the origin.
I'll find AB, but you have to do the other two.

$\displaystyle \text{distance} = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\displaystyle d = \sqrt{(2-1)^2+(6-3)^2}$

$\displaystyle d = \sqrt{1^2+3^2}$

$\displaystyle d = \sqrt{1+9} = \sqrt{10}$

so the distance between a and b is $\displaystyle \sqrt{10}$ or if you want a decimal, it's $\displaystyle \approx 3.1623$

(b)Show that the points O,A,B lie on a straight line.
How do we show these are on the same line? Well, we can do so by showing that it's the same slope between any two points.

So find the slope between O and A

Then find the slope between O and B

If they're the same then they are on the same line.

(c) What is the relationship between point A and the line of segment?
I can spot it from reading the question, but I'm not supposed to give you the answer.

Try drawing it out, and you will notice point A lies in a particular spot on the segment...

3. Originally Posted by helloying
A(1,3) and B(2,6) are points on a coordinate plane.

(a)Find the lenght of OA,OB,AB where O is the origin.
(b)Show that the points O,A,B lie on a straight line.
(c) What is the relationship between point A and the line of segment?
Edit: Too quick, Quick!

If they're so easy, why haven't you completed them?

Use the distance formula to find the distance between two points $\displaystyle (x_1, y_1), (x_2, y_2)$

$\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

To show that points O, A, and B are collinear, make sure the slope of OA=slope of AB= slope of OB.

slope=$\displaystyle \frac{y_2-y_1}{x_2-x_1}$

4. I know how to solve for the dist. of AB but i dont know for O. becos they the question never say where O is? How to solve the distance between OA??

5. Originally Posted by helloying
I know how to solve for the dist. of AB but i dont know for O. becos they the question never say where O is? How to solve the distance between OA??
O's coordinates are (0,0)

6. How do you know??

7. Originally Posted by helloying
How do you know??
By definition, the coordinates of the origin are always (0, 0).