|
Question 769494: Came across this in the Preliminaries for Calculus 7th Edition and am stuck have the line graphed and point given plotted just am stuck on my next move and what the formula/equation to use is.
The point P lies on the x-axis and the point Q lies on the line y=-2x. The point (2,1) is the midpoint of PQ. Find the coordinates of P.
Answer by John10(297)   (Show Source):
You can put this solution on YOUR website! The point P lies on the x-axis and the point Q lies on the line y=-2x. The point (2,1) is the midpoint of PQ. Find the coordinates of P.
------------------------------------------
If you plot any point on the x-axis, the point ALWAYS has the form (x, 0). So point P is (x,0). The midpoint formula is:
((x1 + x2)/2 , (y1 + y2)/2 ) = (2, 1)
where (x1, y1) is point P and (x2, y2) is the point Q.
so
(x1 + x2)/2 = 2 AND (y1 + y2)/2 = 1
x1 + x2 = 4 AND y1 + y2 = 2
Since we know y1 = 0 then 0 + y2 = 2 or y2 = 2
So the point Q is (x, 2). We also know point Q is on the y = -2x
if y = 2 then -2x = 2 or x = -1 (this is x2)
Now we know all coordinate of point Q which is (-1, 2)
Since we know y1, y2, x2, we can find x1:
x1 + x2 = 4
x1 + -1 = 4
x1 = 5
Thus point P is (5,0)
Hope it helps.
If you need some more explanation, please email me at my profile (john100185@yahoo.com)
Sincerely
|
|
|
| |
