# Find Coordinates of Q

• Jun 15th 2009, 03:49 PM
magentarita
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)
• Jun 15th 2009, 04:06 PM
Jhevon
Quote:

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 $Q = (x,y)$

then, $\text{Midpoint (PQ)} = (8,5) = \left( \frac {x + 7}2, \frac {y - 4}2 \right)$

now equate the corresponding coordinates and solve for $x$ and $y$
• Jun 15th 2009, 05:27 PM
magentarita
Do you....
Quote:

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

Let $Q = (x,y)$

then, $\text{Midpoint (PQ)} = (8,5) = \left( \frac {x + 7}2, \frac {y - 4}2 \right)$

now equate the corresponding coordinates and solve for $x$ and $y$

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?
• Jun 15th 2009, 05:32 PM
Jhevon
Quote:

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