Final answer:
The coordinates of the point where the y-coordinate is twice the square of the x-coordinate and lies on the line 5x - 2y = 1 are found by solving the equation 4x² - 5x + 1 = 0. The correct coordinates are B. (-1, -3).
Step-by-step explanation:
To find the coordinates of the point where the y-coordinate is twice the square of the x-coordinate, and which lies on the line with equation 5x - 2y = 1, we need to set up an equation based on the given condition. We are told that y = 2x². By substituting this into the equation of the line, we obtain 5x - 2(2x²) = 1, which simplifies to 5x - 4x² = 1. Next, we rearrange the equation to standard form: 4x² - 5x + 1 = 0. This is a quadratic equation that we can solve by factoring or using the quadratic formula. Upon solving, we find two possible values of x, and then, we can calculate the corresponding y-values since y = 2x².
We test the solutions given in the multiple choices provided:
- A. (1, 1) - Substituting x = 1 into 5x - 2y = 1 gives 5 - 2(1) = 3, which is not equal to 1. So, choice A is incorrect.
- B. (-1, -3) - Substituting x = -1 into 5x - 2y = 1 gives -5 - 2(-3) = 1, which is correct. So, choice B is correct.
- C. (2, 8) - Substituting x = 2 into 5x - 2y = 1 gives 10 - 2(8) = -6, which is not equal to 1. So, choice C is incorrect.
- D. (3, 17) - Substituting x = 3 into 5x - 2y = 1 gives 15 - 2(17) = -19, which is not equal to 1. So, choice D is incorrect.
Therefore, the coordinates of the point are B. (-1, -3).