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?
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 $\displaystyle \approx 3.1623$
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.(b)Show that the points O,A,B lie on a straight line.
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.
I can spot it from reading the question, but I'm not supposed to give you the answer.(c) What is the relationship between point A and the line of segment?
Try drawing it out, and you will notice point A lies in a particular spot on the 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=$\displaystyle \frac{y_2-y_1}{x_2-x_1}$