Thread: Find Coordinates of Q

I come across problems like this all the time. How does one find the coordinates of a given variable on a line segment when one point and the midpoint are given? What is the easiest way to do this?

Suppose that P is the endpoint of a segment PQ and M is the midpoint of PQ. Find the coordinates of Q.

P(7, -4), M(8,5)

Originally Posted by magentarita

I come across problems like this all the time. How does one find the coordinates of a given variable on a line segment when one point and the midpoint are given? What is the easiest way to do this?

Suppose that P is the endpoint of a segment PQ and M is the midpoint of PQ. Find the coordinates of Q.

P(7, -4), M(8,5)

just use the midpoint formula. plug in what you know, and solve for what you don't know.

Let

then,

now equate the corresponding coordinates and solve for and

Originally Posted by Jhevon

just use the midpoint formula. plug in what you know, and solve for what you don't know.

Let

then,

now equate the corresponding coordinates and solve for and

Do you mean like this?

8 + 7/2 = y - 4/2

15/2 = y - 4/2

30 = 2y - 8

30 - 8 = 2y

22 = 2y

22/2 = y

11 = y

Now do the same for x?

Yes or no?

Originally Posted by magentarita

Do you mean like this?

8 + 7/2 = y - 4/2

15/2 = y - 4/2

30 = 2y - 8

30 - 8 = 2y

22 = 2y

22/2 = y

11 = y

Now do the same for x?

Yes or no?

no. i said equate corresponding components. that is, x-component with x-component and y-component with y-component

thus you have:

8 = (x + 7)/2

and

5 = (y - 4)/2

now you can find x and y