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Finding point C in a parabola?
Hi my problem is a graph of a parabola y=x^2
They show a line going through the parabola.Point (1,1) is in the parabola,point (0,2) is in the middle not touching any thing beside the line going through(this is the mid point of the line).The last point is point c who is touching the last left side of the parabola.A line is going through all 3 points including the unknown C.I have tried the midpoint formula to find C put I have not been successful as the answer is (-2,4).I'm just really confused on why that is the answer, when using the mid point formula should word as the mid point and the first point were given.I'm sorry if what I wrote does not make any sense. Thank you for the help and I look forward to the explanation of why the answer for c is (-2,4)
2 Answers
- ignoramusLv 77 years agoFavorite Answer
So you have a straight line through the points (0, 2) and (1, 1)?
Where does the mid-point formula come into it? There is no mention of mid-point in the question. And if you have drawn a diagram of the situation, it should be clear that the point (0,2) is NOT the mid-point of the line. Do NOT assume anything.
Use the formula
(y - y1) . . .(x - x1)
------------ = -----------
(y2 - y1) . .(x2 - x1)
to find the formula of the line. So,
y - 2 . . . . x - 0
------- . = . --------
1 - 2 . . . . 1 - 0
y - 2 = -x
y = 2 - x
Now, this line crosses the parabola y = x² when
2 - x = x²
Rearranging,
x² + x - 2 = 0
(x - 1) (x + 2) = 0
So x = 1, or x = -2
You already know the point (1, 1), so the second point, C is when x = -2, when y = 2 - x, that is y = 4.
So the coordinates of C are (-2, 4)
