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3 years ago

Slope=-4, y-intercept=-5

Mathematics

1 answer:

ra1l [238]3 years ago

8 0

Answer:

Y=-4x-5

Step-by-step explanation:

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Maggie graphed the image of a 90 counterclockwise rotation about vertex A of . Coordinates B and C of are (2, 6) and (4, 3) and

Lemur [1.5K]

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates $(x_A,y_A)$

Vectors AB and AB' are perpendicular, then

$\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0$

Vectors AC and AC' are perpendicular, then

$\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0$

Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$

Then

$y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2$

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

8 0

3 years ago

4,11,6,9,23,34,6,9

ludmilkaskok [199]

Answer: 9

Step-by-step explanation:

If you put all the numbers in order from least to greatest 9 is in the middle.

4 0

3 years ago

Read 2 more answers

Help me please it’s due by today

anyanavicka [17]

Answer:

Step-by-step explanation:

Lateral SA = area of the 4 triangles

Formula to be used :-

Area (triangle) = 1/2bh

=> 4 x 1/2 x 9 x 12

=> 108 x 2

=> 216 cm²

Total SA = LSA + area of the square

Formula to be used :-

Area (square) = side length x side length

=> 216 + 9 x 9

=> 216 + 81

=> 297 cm²

<u>The correct option is (D).</u>

4 0

2 years ago

What is the length of chord An in Oo below?

Anika [276]

Answer:

12 units

Step-by-step explanation:

$In\: \odot O,$

chords $\overline{ML}$ and $\overline{AN}$ are equidistant (7.2 units) from the center of the circle O.
Measures of the chords equidistant from the center of the circle are equal.
$\therefore m(chord\:\overline{AN}) =m(chord\:\overline{ML})$
$\because m(chord\:\overline{ML}) = 12\: units$
$\therefore m(chord\:\overline{AN}) = 12\: units$