ABCD∼EFGH

AD=45 in. , EH=75 in. , and AB=30 in.

What is EF ?

Enter your answer in the box.

EF =
in.

Also Triangle ABC undergoes a series of transformations to result in triangle DEF .

Is triangle DEF congruent to triangle ABC ?

Select Congruent or Not congruent for each description.

Description Congruent Not congruent
Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF.
Triangle ABC is rotated 180°, and then translated 4 units down and 2 units right to form triangle DEF.

and
A point at (−1, 10) is rotated 90° counterclockwise about the origin.

What are the coordinates of the resulting image?

(−1, −10)

(1, −10)

(−10, −1)

(10, 1)

Question

08-03-2018
Mathematics

contestada

ABCD∼EFGH

AD=45 in. , EH=75 in. , and AB=30 in.

What is EF ?

Enter your answer in the box.

EF =
in.

Also Triangle ABC undergoes a series of transformations to result in triangle DEF .

Is triangle DEF congruent to triangle ABC ?

Select Congruent or Not congruent for each description.

Description Congruent Not congruent
Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF.
Triangle ABC is rotated 180°, and then translated 4 units down and 2 units right to form triangle DEF.

and
A point at (−1, 10) is rotated 90° counterclockwise about the origin.

What are the coordinates of the resulting image?

(−1, −10)

(1, −10)

(−10, −1)

(10, 1)

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jamuuj jamuuj · Answer 1 · 2018-03-19T08:14:54+01:00

1. For similar triangles, the ratio of the corresponding sides is constant.
In this case, AD corresponds to EH, while AB corresponds to EF.
Therefore; AD/EH = AB/EF
45/75 = 30/ EF
EF = (30×75)/45
= 50 in

2. Triangle DEF is not congruent ABC.
For congruent triangles; if three pairs of sides are equal in length, then the triangles are congruent. Also triangles are congruent if two pairs of angles of the triangle are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

3. Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF. This description is Congruent.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF. Description not congruent
Triangle ABC is rotated 180° , and then translated 4 units down and 2 units right to form triangle DEF. The description is Congruent

4. A point (-1,10) is rotated 90° counterclockwise about the origin.
The resulting coordinates of the image is (-10,-1)
A rotation through 90 about the origin is anticlockwise (counter clockwise direction)