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2 years ago

10

Triangle QRS is translated 7 units right, then rotated 90 degrees clockwise about the origin. The vertices of triangle Q"R"S" ar

e Q"(6, -1), R"(0, -1), and S"(0, -7). Determine the coordinates of triangle QRS

1 answer:

Goryan [66]2 years ago

7 0

Answer:

Q (-6.6), R (-6.0), S (0.0)

Step-by-step explanation:

In the exercise we are asked to find the original coordinates with the given transforms, which means that we must apply the inverse of the indicated transformations.

Original coordinates: Q "(6, -1), R" (0, -1) and S "(0, -7)

When turning 90 ° counterclockwise, since we want the opposite, the following change occurs (the axes and the sign are inverted):

Q '(1.6), R' (1.0), S '(7.0)

Now we have to move to the left by 7 units, because it is the opposite of the right, only on the x axis, 7 is subtracted

Q (-6.6), R (-6.0), S (0.0)

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1 year ago

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

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Here is the question attached with.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ is a straight line.

$\angle AEF$ is a right angled triangle.

Options $1,4,5,6$ are correct answers.

Step-by-step explanation:

⇒As $\ ray\ AE$ is ⊥ $FEC$ so it will forms right angled triangle then $m\angle CEA =90\ (deg)$ .

⇒Measure of $\angle BEF =135\ (deg)$ as $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ is the bisector of $\angle AEC$ ,meaning that $\angle AEB$ is half of $\angle AEC$ so $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ is a straight line as the angles measure over it is $180\ (deg)$ .

⇒Measure of $\angle AEF = 90\ (deg)$ from linear pair concept.

As $\angle CEA + \angle AEF = 180\ (deg)$ ,plugging the values of $m\angle CEA =90\ (deg)$ we have $\angle AEF = 90\ (deg)$ .

The other two options are false as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it is exceeding $180\ (deg)$ whereas $\angle CEF$ is a

straight line.

And $m\angle CEB=2(m\angle CEA)$ is not true.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

So we have total $4$ answers.

The correct options are $1,4,5,6$ .

5 0

2 years ago

Read 2 more answers