Endpoint

[Shadowgurl]

The coordinates of point T are given. The midpoint of ST is (5, 28). Find the
coordinates of point S.


T(0, 4)


So how do you find the endpoint when the midpoint is given?

 

[pka]

The coordinates of point T are given. The midpoint of ST is (5, 28). Find the
coordinates of point S.
T(0, 4)
So how do you find the endpoint when the midpoint is given?

The midpoint between $\displaystyle \left(t_x,t_y\right)~\&~\left(s_x,s_y\right)$ is $\displaystyle \left(\dfrac{t_x+s_x}{2},\dfrac{t_y+s_y}{2}\right)$.

In other words, just average the coordinates.

 

[lookagain]

The midpoint between $\displaystyle \left(t_x,t_y\right)~\&~\left(s_x,s_y\right)$ is $\displaystyle \left(\dfrac{t_x+s_x}{2},\dfrac{t_y+s_y}{2}\right)$.

In other words, just average the coordinates.

Yes, pka, but how would you explain how to apply this formula to Shadowgurl regarding the needed coordinates of the endpoint, as opposed to the midpoint?

 

[pka]

Yes, pka, but how would you explain how to apply this formula to Shadowgurl regarding the needed coordinates of the endpoint, as opposed to the midpoint?

I would not explain it. She will learn so much more if she tries to apply the concept to given.

 

[wjm11]

The coordinates of point T are given. The midpoint of ST is (5, 28). Find the
coordinates of point S.


T(0, 4)


So how do you find the endpoint when the midpoint is given?

PKA has provided information to approach the problem algebraically. Let's try another approach to understanding this problem.

Using graph paper, make an xy graph and plot the two points T(0,4) and M(5,28). [If you do not have graph paper, you can still make a sketch of this graph and points to help you understand.]

Place your pencil on point T. Move your pencil to the right 5 units. The pencil is now directly under the midpoint M. Now move your pencil straight up 24 units. You are now on the midpoint, M.

If you repeat these moves starting at point M (going 5 to the right, then 24 up) you will be at the other end point, S.

Does this make sense to you?

Ask yourself: How did we know how far to move each time? Well, look at the x and y values of points T and M. For the x direction, we have 5 - 0 = 5. For the y direction, we have 28 - 4 = 24. Thus, if we add those values to the point M values, we end up at the other end point: 5 + 5 = 10 (for x) and 28 + 24 = 52 (for y).

To see this method applied algebraically, try here: http://www.algebra.com/algebra/home...e/Length-and-distance.faq.question.95094.html

 

[lookagain]

The midpoint between $\displaystyle \left(t_x,t_y\right)~\&~\left(s_x,s_y\right)$ is $\displaystyle \left(\dfrac{t_x+s_x}{2},\dfrac{t_y+s_y}{2}\right)$.

> > In other words, just average the coordinates. < <

This is why I picked on you. If I had seen your answer first before the OP's question, then I would have highly expected the OP to be asking on how to find the midpoint, not an endpoint. And the part of your post that cements that notion for me is the last sentence highlighted above.