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2 years ago

The point A (-5, -2) is reflected over the line y = -1, and then is reflected over the line x = 3. What are the coordinates of A

2 answers:

8 0

When A is reflected over y=-1, -1+(-1-(-2))=0, it lands on (-5, 0), when it is then reflected over x=3, 3+(3-(-5))=11, it lands on (11,0)
If you can't visualize it, draw a graph.

ollegr [7]2 years ago

6 0

Answer:

(11,0)

Step-by-step explanation:

A is (-5,-2)

It is reflected over the line y=-1

The distance between the y value is -1-(-2)= 1

So we move 1 unit above the line y=-1

After reflection over the line y=-1 the A becomes (-5,1-1) is (-5,0)

It is reflected over the line x = 3

The distance between -5 and 3 is $3-(-5)= 8$

So we move 8 units away from the line x=3

Point (-5,0) becomes (3+8,0) is (11,0)

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alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS

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Answer:

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Step-by-step explanation:

We are given $\alpha$ and $\beta$ are zeros of the polynomial $x^2-(k+6)x+2(2k-1)$ .

We want to find the value of $k$ if $\alpha+\beta=\frac{1}{2}$ .

Lets use veita's formula.

By that formula we have the following equations:

$\alpha+\beta=\frac{-(-(k+6))}{1}$ (-b/a where the quadratic is ax^2+bx+c)

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Let's simplify those equations:

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If $\alpha+\beta=k+6$ and $\alpha+\beta=\frac{1}{2}$ , then $k+6=\frac{1}{2}$ .

Let's solve this for k:

Subtract 6 on both sides:

$k=\frac{1}{2}-6$

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$k=\frac{1}{2}-\frac{12}{2}$

Simplify:

$k=\frac{-11}{2}$ .

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2 years ago

Consider the diagram and proof by contradiction.

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