Mathematics, 13.09.2019 18:10 jaymoria16

90 points!
which statement is correct for triangle abc. and triangle a prime b prime c prime.?
triangle abc is similar to triangle a prime b prime c prime., because triangle a prime b prime c prime. is obtained by dilating triangle abc. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
triangle abc is similar to triangle a prime b prime c prime., because triangle a prime b prime c prime. is obtained by dilating triangle abc. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
triangle abc is similar to triangle a prime b prime c prime., because triangle a prime b prime c prime. is obtained by dilating triangle abc. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
triangle abc is similar to triangle a prime b prime c prime. because triangle a prime b prime c prime. is obtained by dilating triangle abc. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees

90 points! which statement is correct for triangle abc. and triangle a prime b prime c prime.

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Answer from: theday2278

The length of AB is 8 units.

The length is A'B' is 2 units.

This is a 1/4 scale:

2/8 = 1/4

AB is at the top of it's image A'B; is at the bottom of it's image, so they are also a mirror image.

Each quadrant would be a 90 degree rotation. A'b" is two quadrants different so would be a 180 degree rotation.

The answer would be:

Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC.by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees

Answer from: mayorga2genesis2

ΔABC is similar to ΔA'B'C'. because ΔA'B'C'. is obtained by dilating ΔABC by a scale factor of 1/4. and then rotating it about the origin by 180°.

Step-by-step explanation:

From the graph, we observe that the triangle was rotate 180°. That means the viable answers are the second and last option.

Now, we also notice that the dilation of the triangle is by a fraction, because it shrank. To find the right scale factor, we just have to compare coordinates.

The coordinates of ΔABC are A(4,-4); B(12,-4); C(8,-12).

The coordinates of ΔA'B'C' are A'(-1,1); B'(-3,1); C'(-2,3).

Notice that if we divide each corresponding coordinates, we have 4 as a scale factor, that is

A. $\frac{4}{-1} =-4\\\frac{-4}{1}=-4$

B. $\frac{12}{-3}=-4\\\frac{-4}{1}=-4$

C. $\frac{8}{-2}=-4\\\frac{-12}{3}=-4$

As you can observe the decreasing scale factor is $\frac{1}{4}$ , because if we divide the coordinates of ΔABC, we obtain the coordinates of ΔA'B'C'. It's important to consider the negative sign, it's part of the transformation.

Therefore, the right answer is the last choice.ΔABC is similar to ΔA'B'C'. because ΔA'B'C'. is obtained by dilating ΔABC by a scale factor of 1/4. and then rotating it about the origin by 180°.

Answer from: Quest

nswer: a y-axis

step-by-step explanation:

Answer from: Quest

$x=-2$ or $x=-5$

step-by-step explanation:

we need to solve for 'x' the following equation: $\sqrt{(x+6)} - 4 = x$

we have that:

$\sqrt{(x+6)} - 4 = x$ ⇒ $(x+6) = (x+4)^{2}$

⇒ $x+6 = x^{2} + 8x + 16$ ⇒ $x^{2} + 7x + 10 = 0$

factorizing, we get that:

$x^{2} + 7x + 10 = 0$ ⇒ $(x+2)(x+5)=0$

then, the solutions are: $x=-2$ or $x=-5$

nothing extraneous has been found!

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90 points!
which statement is correct for triangle abc. and triangle a prime b prime c prime....