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3 years ago

If the endpoints of `bar(AB)` have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of `bar(AB)`?

Mathematics

1 answer:

alina1380 [7]3 years ago

5 0

To solve this problem you must apply the proccedure shown below:

1. You have the following points given in the problem above:

$A(9,8)\\ B(-1,-2)$

2. To find the midpoint, you must apply the formula that is used for calculate it. This is:

$m=(\frac{x1+x2}{2}, \frac{y1+y2}{2} )$

Where:

$x1=9\\ x2=-1\\ y1=8\\ y2=-2$

3. Now, you must substitute these values into the formula for calculate the midpoint, as following:

$m=(\frac{9+(-1)}{2} ,\frac{8+(-2)}{2} )\\ m=(4,3)$

Therefore, the answer is: $m=(4,3)$

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Answer:

Step-by-step explanation:

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Check the forward differences of the sequence.

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$b_{n+1} = b_n + 2$

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and so on down to

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We solve for $a_n$ in the same way.

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Then

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$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

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2 years ago

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Answer:

Step-by-step explanation:

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