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Natalija [7]
3 years ago
6

Show that AC and BD bisect each other if A(–3, –5), B(2, –3), C(3, 5), and D(–2, 3). Find AC and BD

Mathematics
2 answers:
Mazyrski [523]3 years ago
7 0

Answer

Multipy all of them

Step-by-step explanation:

mulitiply all of them

Mashcka [7]3 years ago
3 0

Answer:

Step-by-step explanation:

midpoint of AC=((-3+3)/2,(-5+5)/2)=(0,0)

midpoint of BD=((2-2)/0,(-3+3)/2)=(0,0)

coordinates  of midpoint of AC and BD are same.

∴ AC and BD bisect each other.

AC=\sqrt{(3-(-3))^2+(5-(-5))^2 } =\sqrt{6^2+10^2} =\sqrt{136} =2\sqrt{39} \\BD=\sqrt{((-2-2)^2+(3-(-3))^2} =\sqrt{16+36} =\sqrt{52} =2\sqrt{13}

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3 years ago
What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?
vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a  =  determines whether the graph opens up or down, and it also makes the parent function <u>wider</u> or <u>narrower</u>.

  • <u>positive</u> value of a = opens <u><em>upward</em></u>
  • <u>negative</u> value of a = opens <u><em>downward</em></u>
  • a is between 0 and 1, (0 < a < 1) the graph is <u><em>wider</em></u> than the parent function.
  • a > 1, the graph is <u><em>narrower</em></u> than the parent function.

<em>h </em>=<em> </em>determines how far left or right the parent function is translated.

  • h = positive, the function is translated <em>h</em> units to the right.
  • h = negative, the function is translated |<em>h</em>| units to the left.

<em>k</em> determines how far up or down the parent function is translated.

  • k = positive: translate <em>k</em> units <u><em>up</em></u>.
  • k = negative, translate <em>k</em> units <u><em>down</em></u>.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)²  -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

8 0
2 years ago
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