SOLUTION: Find the other endpoint of a line segment with the given midpoint and one endpoint (I need major help on these) Endpoint: ( 6, -1); Midpoint: (15/2, 2) A. (9,5) B. (2, 15/2)

Algebra ->  Equations -> SOLUTION: Find the other endpoint of a line segment with the given midpoint and one endpoint (I need major help on these) Endpoint: ( 6, -1); Midpoint: (15/2, 2) A. (9,5) B. (2, 15/2)       Log On


   

Question 318144: Find the other endpoint of a line segment with the given midpoint and one endpoint (I need major help on these)
Endpoint: ( 6, -1); Midpoint: (15/2, 2)
A. (9,5) B. (2, 15/2) C. (-3, -6) D. (15,4)
Use the discriminant to determine how many real-number solutions the equation has.
v2 - 7v + 5 = 0
A. 2 B. 1 C. 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The midpoint of the points (a,b) and (c,d) is (p,q) where p=%28a%2Bc%29%2F2 and q=%28b%2Bd%29%2F2. In this case, a=6, b=-1, p=15%2F2 and q=2. Plug these values in to get:

15%2F2=%286%2Bc%29%2F2 and 2=%28-1%2Bd%29%2F2

I'll let you solve those equations.

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From v%5E2-7v%2B5 we can see that a=1, b=-7, and c=5


D=b%5E2-4ac Start with the discriminant formula.


D=%28-7%29%5E2-4%281%29%285%29 Plug in a=1, b=-7, and c=5


D=49-4%281%29%285%29 Square -7 to get 49


D=49-20 Multiply 4%281%29%285%29 to get %284%29%285%29=20


D=29 Subtract 20 from 49 to get 29


Since the discriminant is greater than zero, this means that there are two real solutions.