Q: Translation by vector (−6−7)

After translation by vector (−6−7) the x-coordinate of vertex is reduce by 6 unit and y-coordinate will reduce by 7 units.here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After translation by vector (−6−7) New coordinates of vertices of image will be (−5,−6),(−2,−6),(−5,−1),(0,−3),(−3,−4)

Q: Identify a specific series of transformations that would take the pre-image (darker in blue) to the image (lighter in green). Then tell whether the pre-image and image are congruent or similar.

Scale factor =510=2here image if enlarge by scale factor 2, but image is opposite side of origin hence S.F will be of -2.Here image is not congruent to pre-image, but they are similar.

Question 1

i2+(−i)2−4i(i−1)=?In the complex number system, what is the value of the given expression? (Note: i=−1​)

Accepted Answer

i2+(−i)2−4i(i−1)=−1−1−4i2+4i=−2−4(−1)+4i=2+4i

Question 2

Write True or False.53=15

Accepted Answer

53=155×5×5125Hence, false.

Question 3

Translation by vector (−6−7​)

Accepted Answer

After translation   by vector (−6−7​) the x-coordinate of vertex is reduce by 6 unit and y-coordinate will reduce by 7 units.here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After translation   by vector (−6−7​) New coordinates of  vertices of image will be (−5,−6),(−2,−6),(−5,−1),(0,−3),(−3,−4)

Question 4

Rotation by 180∘

Accepted Answer

here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After rotation by 180∘:x′=−x, and y′=−yso vertices of image will be (−1,−1),(−4,−1),(−1,−6),(−6,−4),(−3,−3)

Question 5

Reflection across the x-axis

Accepted Answer

here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After Reflection across the x-axis :x′=x, and y′=−yso vertices of image will be (1,−1),(4,−1),(1,−6),(6,−4),(3,−3)

Question 6

Dilation by scale factor 21​

Accepted Answer

here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After Dilation by scale factor 21​ :x′=21​x, and y′=21​y so vertices of image will be (21​,21​),(2,21​),(21​,3),(3,2),(23​,23​)

Question 7

Translation by vector (2−2​) and rotation by 90∘

Accepted Answer

here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After Translation by vector (2−2​) :x′=x+2, and y′=y−2 so vertices of image will be (3,−1),(6,−1),(3,4),(8,2),(5,1) After rotation by 90∘ :x′=−y, and y′=x so vertices of image will be (1,3),(1,6),(−4,3),(−2,8),(−1,5)  Here image and pre-image are congruent.

Question 8

Rotation by 180∘ and reflect across y-axis

Accepted Answer

Here vertices of pre-image are (1,1),(4,1),(1,6),(6,4),(3,3)After rotation by 180∘:x′=−x, and y′=−yso vertices of image will be (−1,−1),(−4,−1),(−1,−6),(−6,−4),(−3,−3)After  reflection across y-axis :x′=−x, and y′=yso vertices of image will be (1,−1),(4,−1),(1,−6),(6,−4),(3,−3) Here image and pre-image are congruent.

Question 9

Identify a specific series of transformations that would take the pre-image (darker in blue) to the image (lighter in green). Then tell whether the pre-image and image are congruent or similar.

Accepted Answer

Pre-image is first reflected in x-axis, then coordinate of vertices become :(1,−1),(4,−1),(1,−6),(6,−4),(3,−3) .And then shows a translation, the coordinate of translated  image is :(−6,8),(−3,8),(−6,3),(−1,5),(−3,3)So the required translation is given by vector (−6−18−(−1)​)=(−79​)Here image and pre-image are congruent.

Question 10

Identify a specific series of transformations that would take the pre-image (darker in blue) to the image (lighter in green). Then tell whether the pre-image and image are congruent or similar.

Accepted Answer

From the fig. it is clear that Pre-image is first rotated by 90∘ and then reflected in x-axis.Here image and pre-image are congruent.

Question 11

Identify a specific series of transformations that would take the pre-image (darker in blue) to the image (lighter in green). Then tell whether the pre-image and image are congruent or similar.

Accepted Answer

Scale factor =510​=2here image if enlarge by scale factor 2, but image is opposite side of origin hence S.F will be of -2.Here image is not congruent to pre-image, but they are similar.

Question 12

Identify a specific series of transformations that would take the pre-image (darker in blue) to the image (lighter in green). Then tell whether the pre-image and image are congruent or similar.

Accepted Answer

First of all pre-image is rotated by 180 degree, then translated by vector  (80​)

Question 13

Determine if the following triangles are similar or not and explain why or why not.

Accepted Answer

The angles of a triangle add up to 180∘m∠G′H′I′=180∘−40∘−30∘=110∘ here one angle in both the triangle are equal but there is no evidence for any other angle to be equal .Hence these two triangles can not be similar.

Question 14

Determine if the following triangles are similar or not and explain why or why not.

Accepted Answer

The angles of a triangle add up to 180∘m∠G′H′I′=180∘−50∘−30∘=100∘ Here we can not say that the any two angles of triangle GHI is equal to corresponding angles of triangle G'H'I'.Hence these two triangles can not be similar.

Question 15

Determine if the following triangles are similar or not and explain why or why not.

Accepted Answer

From the first triangle GHI sum of remaining two angles =180∘−110∘=70∘From the first triangle G'H'I' sum of remaining two angles =180∘−130∘=50∘It is clear that remaining two angles of  triangle GHI can not be equal to corresponding angles of triangle G'H'I'.Hence these two triangles can not be similar.

Question 16

What type of angles are ∠1 and ∠4 ?

Accepted Answer

∠1 and ∠4 are pair of vertical angles.

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