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Pachacha [2.7K]
2 years ago
14

How to verify midpoint using distance formula

Mathematics
1 answer:
Brut [27]2 years ago
7 0

Answer:


Step-by-step explanation:

Suppose you draw line AC and calculate the midpoint of AC.

To verify the correctness of your midpoint, you'd find the distance from A to the midpoint, M, as well as the distance from the midpoint, M, to C.  If these two distances are equal, then you've found that your midpoint calculation was correct.

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A right triangle has one vertex on the graph of y = 9 - x^2 , x > 0, at ( x , y ), another at the origin, and the third on th
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  d.  x = √3; A(√3) = 3√3

Step-by-step explanation:

a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...

  A(x) = (1/2)(x)(y)

  A(x) = (1/2)(x)(9-x^2)

__

b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).

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__

c. A(2) = (1/2)(2)(9 -2^2) = 5

The area is 5 when x=2.

__

d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).

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