SOLUTION: 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/equatio

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
RELATED QUESTIONS
When plotte on the rectangular coordinate system, in which quadrant would the following... (answered by scott8148)

Use the given conditions to write an equation for the line in point-slope form. Slope... (answered by Alan3354)

I needed to find the slope of a graphed line. I came up with the following values x,y... (answered by Earlsdon)

I am taking Applied Calculus - for the Managerial, Life and Social Sciences. It has been (answered by jim_thompson5910)

Use the given conditions to write an equation for the line in point-slope form. Slope... (answered by rfer,Alan3354)

Hello! I was having difficulty answering two out of three questions I was given:... (answered by jim_thompson5910)

I understand how you answer the Questions that say: Write an equation of the line that... (answered by solver91311,edjones)

The directions say this: "Find the value of x or y so that the line through the points... (answered by Alan3354,It is costly,MathTherapy)

Hello, I managed to find the solution to this question through trial and error, but I am... (answered by bucky)