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3 years ago

Which rule describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E"?

Mathematics

2 answers:

Trava [24]3 years ago

7 0

Answer:

ABCDE is first transformed into A'B'C'D'E' after a reflection along m line. Then a rotation of 180° about C' is made and A"B"C'D"E" is gotten.

Step-by-step explanation:

In a reflection, the distance between the original point and the reference line is equal to the distance between the reflected point and the reference line.

meriva3 years ago

4 0

The composition of transformations that maps figure ABCDE to figure ${\text{A''B''C'D''E''}}$ is $\boxed{{\text{a reflection about line }}m{\text{ the rotate 18}}{{\text{0}}^ \circ }}.$

Further explanation:

The rule of transformation of the coordinates can be expressed as follows,

$\boxed{\left( {x,y} \right) \to \left( {kx,ky} \right)}$

Isometry is a mapping of space to another space so that the length between the points is same as the length in the original space. Translation and the rotation are the isometries of plane.

Explanation:

In isometric transformation the shape of the original and the image remains the same and the size of the image is same as the original.

From the attached figure it has been observed that the composition of transformations that maps figure ABCDE to figure ${\text{A''B''C'D''E''}}$ is first reflect the polygon ABCDE about line $m$ and then rotate about 180 degree anti clockwise.

The composition of transformations that maps figure ABCDE to figure ${\text{A''B''C'D''E''}}$ is $\boxed{{\text{a reflection about line }}m{\text{ the rotate 18}}{{\text{0}}^ \circ }}.$

Learn more:

Learn more about inverse of the functionhttps://brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: image vertices, triangle, dilated, lies, same line, shift four units, left, pre-imaged, dilation, center, scale factor, four, coordinates, x-coordinates, y-coordinate, transformation rule.

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Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.

marshall27 [118]

Answer:

$\lim _{x\to 2}\:\frac{x-2}{x^2-2}\\\\ \lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}\\\\ \lim _{x\to \frac{5}{2}}\left\frac{2x^2+x-15}{2x-5}\right$

Step-by-step explanation:

a) $\lim _{x\to 3}\:\frac{x^2-10x+21}{x^2+4x-21}=\lim \:_{x\to \:3}\:\frac{\left(x-7\right)\left(x-3\right)}{\left(x+7\right)\left(x-3\right)}=\lim \:_{x\to \:3}\:\frac{x-7}{x+7}=\frac{3-7}{3+7}=-\frac{4}{10}=-\frac{2}{5}$

b) $\lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=\lim \:_{x\to -\frac{3}{2}}\:\frac{\left(2x+3\right)\left(x-4\right)}{\left(2x+3\right)}=\lim \:\:_{x\to \:-\frac{3}{2}}\:\left(x-4\right)=-\frac{3}{2}-4\\ \\ \lim _{x\to -\frac{3}{2}}\left(\frac{2x^2-5x-12}{2x+3}\right)=-\frac{11}{2}$

c) $\lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0$

d) $\lim _{x\to 11}\:\frac{x^2+6x-187}{x^2+3x-154}=\lim _{x\to 11}\:\frac{\left(x-11\right)\left(x+17\right)}{\left(x-11\right)\left(x+14\right)}=\lim _{x\to 11}\:\frac{\left(x+17\right)}{\left(x+14\right)}=\frac{11+17}{11+14}=\frac{28}{25}$

e) $\lim _{x\to 3}\:\frac{x^2-8x+15}{x-3}=\lim \:_{x\to \:3}\:\frac{\left(x-3\right)\left(x-5\right)}{x-3}=\lim _{x\to 3}\left(x-5\right)=3-5=-2$

f) $\lim _{x\to \frac{5}{2}}\left(\frac{2x^2+x-15}{2x-5}\right)=\lim \:_{x\to \:\frac{5}{2}}\frac{\left(2x-5\right)\left(x+3\right)}{2x-5}=\lim \:\:_{x\to \:\:\frac{5}{2}}\left(x+3\right)=\frac{5}{2}+3=\frac{11}{2}$