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SVEN [57.7K]
2 years ago
11

I need help with this geometry question, matching the right ones to each other.

Mathematics
1 answer:
8090 [49]2 years ago
3 0

The transformations and their respective descriptions are:

A. (x, y) ⇒ (3x, y) implies horizontal stretch by a scale factor of 3

B. (x, y) ⇒ (x+3, y) implies translation 3 units right

C. (x, y) ⇒ (x, 3y) implies vertical stretch by a factor of 3

D. (x, y) ⇒ (x, y+3) implies  implies translation 3 units up

E. (x, y) ⇒ (3x, 3y) implies dilation with a scale factor 3

<h3>What is Translation?</h3>

Translation is an algebraic transformation of a shape by moving the vertices some units along the x or y axis.

When a shape is translated it may move to a new position depending on the orientation of the translation.

Analysis:

For A, the x coordinate was transformed three times its initial value stretching it horizontally.

For B, the x coordinate moved 3 units further away from its initial value making the new value x+3 and y remaining the same.

For C, the y coordinated was transformed to a value three times what it was, making it to be stretched vertically, since the y-axis is a vertical axis.

For D, the y coordinate was moves 3 units away from its initial position making it to be translated up, since 3 is positive.

For E, both coordinates were stretched 3 units as much as their original value making the shape to dilate.

Learn more about linear transformations: brainly.com/question/13005179

#SPJ1

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The triangular prism has a volume of 27 cubic units.
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Given:

The volume of the triangular prism = 27 cubic units

To find the volume of the prism if each side is dilated by \frac{1}{3}

Formula

The volume of a triangular prism

V = \frac{1}{2} ach

where, a be the height of the triangle

c be the base of the triangle

h be the height of the prism

Let us take after dilation the we get,

a \rightarrow \frac{1}{3} a

c \rightarrow \frac{1}{3} c and

h \rightarrow \frac{1}{3} h

So,

After dilation the volume will be

V_{1} =\frac{1}{2}  (\frac{a}{3}  )(\frac{c}{3} )(\frac{h}{3} )

or, V_{1} =\frac{1}{9} (\frac{1}{2} ach)

or, V_{1}=\frac{1}{9}  (27) [Since, V = \frac{1}{2} ach = 27]

or, V_{1} = 3

Hence,

After dilation the volume of the prism will be 3 cubic unit.

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In the diagram, .
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Given: In triangles PMN and QSR :

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From (1)

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