In order to find the second endpoint or a line segment given the first and the midpoint, you need to realize that the midpoint is an average of the two endpoints. Given that fact, we can derive this formula looking at x values of points A and B with midpoint M. Remember this is only looking at the x values.
(A + B)/2 = M
So if we are looking for A, we can solve for A and use this modified formula.
(A + B)/2 = M
A + B = 2M
A = 2M - B
Now we can do this with the y values of these points as well. We then have the coordinates of both parts of A.
Answer:
Step-by-step explanation:
All Done!
Answer:
6.28
Step-by-step explanation:
2 x 3.14
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
