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rodikova [14]
2 years ago
15

How do you find endpoints of a line segment with a given endpoint and midpoint?

Mathematics
1 answer:
seraphim [82]2 years ago
6 0

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.

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Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart
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Answer:

b; ∀x   P(x) ∨ ¬P(x)

Step-by-step explanation:

Suppose that we have a proposition p

Such that p can be true or false.

We can define the negation of p as:

¬p

Such that, if p is false, then ¬p is true

if p is true, then ¬p is false.

Also remember that a proposition like:

p ∨ q

is true when, at least one, p or q, is true.

Then if we write:

p ∨ ¬p

Always one of these will be true (and the other false)

Then the statement is true.

And if the statement depends on some variable, then we will have that:

p(x) ∨ ¬p(x)

is true for all the allowed values of x.

from this, we can conclude that the statement that is always true is:

b; ∀x   P(x) ∨ ¬P(x)

Where here we have:

For all the values of x,   P(x)  ∨ ¬P(x)

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2 years ago
What is equation of a line that is parallel to y = -6x – 1 and passes through the point (1,4)
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Answer:

y = -6x + 10

Step-by-step explanation:

Parallel lines share the same slope.  Given y = -6x – 1, we know that the equation of this new line has the form y = -6x – C.  The coordinates of the point (1, 4) determine the value of C:

(4) = -6(1) – C, or:

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