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3 years ago

10

What series of transformations map triangle △ABC onto △EDF to prove that ABC≅EDF ?

2 answers:

Nonamiya [84]3 years ago

7 0

Hello!

The correct answer is A translation 3 units up then a reflection across the x-axis.

Translation: moving/sliding a figure
Reflection: taking a figure and flipping it over a line.

kondaur [170]3 years ago

4 0

Answer:

translation 3 units down then a reflection across x-axis

Step-by-step explanation:

A translation is a kind of rigid motion . It trace a function that maps an object a particular distance.
A reflection is a kind of rigid motion . It is mainly a flips of a shape across the line of reflection.

In the given figure, we can see that Δ ABC is vertically 3 units away from the x axis .

So we translate Δ ABC by 3 units down and then reflect it across x axis to get ΔDEF.

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Find values of  that satisfy the equation for 0º    360º and 0  θ  2 . Give answers in degrees and radians.

suter [353]

Answer:

$\theta = 30^\circ, 330^\circ$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

Step-by-step explanation:

Given [Missing from the question]

Equation:

$cos\theta = \frac{\sqrt 3}{2}$

Interval:

$0 \le \theta \le 360$

$0 \le \theta \le 2\pi$

Required

Determine the values of $\theta$

The given expression:

$cos\theta = \frac{\sqrt 3}{2}$

... shows that the value of $\theta$ is positive

The cosine of an angle has positive values in the first and the fourth quadrants.

So, we have:

$cos\theta = \frac{\sqrt 3}{2}$

Take arccos of both sides

$\theta = cos^{-1}(\frac{\sqrt 3}{2})$

$\theta = 30$ --- In the first quadrant

In the fourth quadrant, the value is:

$\theta = 360 -30$

$\theta = 330$

So, the values of $\theta$ in degrees are:

$\theta = 30^\circ, 330^\circ$

Convert to radians (Multiply both angles by $\pi/180$ )

So, we have:

$\theta = \frac{30 * \pi}{180}, \frac{330 * \pi}{180}$

$\theta = \frac{\pi}{6}, \frac{33 * \pi}{18}$

$\theta = \frac{\pi}{6}, \frac{11 * \pi}{6}$

$\theta = \frac{\pi}{6}, \frac{11\pi}{6}$

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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