Question 769494
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.

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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.

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Sincerely