Biology : asked on jdenty3398
 12.03.2021

Draw the image of ABC under a translation by 1 unit to the left and 5 units up.

. 4

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Mathematics
Step-by-step answer
P Answered by Specialist
On all points a,b,c move one unit to the left and five units up and draw a dot where it ends. then connect all 3 points to get the translation
Mathematics
Step-by-step answer
P Answered by Specialist
On all points a,b,c move one unit to the left and five units up and draw a dot where it ends. then connect all 3 points to get the translation
Mathematics
Step-by-step answer
P Answered by Specialist
12. C ends up where A is, at (3, 3).
13. Straight across is 180°.
14. Following one point through this translation leads you to triangle KLM.
15. Since P is 3 units right of x = -3, it will end up 3 units left of it, at -6. As it's 4 units down from y = 4, it will end up 4 units above it, at 8. (-6, 8)
16. It appears to be the same as a translation (it's flipped twice and ends up in the same orientation).

Need clarification?
Mathematics
Step-by-step answer
P Answered by Specialist
12. C ends up where A is, at (3, 3).
13. Straight across is 180°.
14. Following one point through this translation leads you to triangle KLM.
15. Since P is 3 units right of x = -3, it will end up 3 units left of it, at -6. As it's 4 units down from y = 4, it will end up 4 units above it, at 8. (-6, 8)
16. It appears to be the same as a translation (it's flipped twice and ends up in the same orientation).

Need clarification?
Mathematics
Step-by-step answer
P Answered by Specialist
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)

             
Mathematics
Step-by-step answer
P Answered by Master
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)

             
Mathematics
Step-by-step answer
P Answered by Specialist

See explanation

Step-by-step explanation:

Given

A = (-1,1)

B  = (3,3)

C =(4,-2)

Solving (a): P(0,0) \to Q(1,3)

This means that:

(x,y) \to (x+1,y+2)

So, we have:

A = (-1,1)

A' = (-1 + 1,1+2)

A' = (0,3)

B  = (3,3)

B'= (3 + 1,3+2)

B'= (4,5)

C =(4,-2)

C' = (4+1,-2+1)

C' = (5,-1)

Solving (b): P(0,-1) \to Q(4,-2)

This means that:

(x,y) \to (x+4,y-1)

So, we have:

A = (-1,1)

A' = (-1+4,1-1)

A' = (3,0)

B  = (3,3)

B'= (3+4,3-1)

B'= (7,2)

C =(4,-2)

C' = (4+4,-2-1)

C' = (8,-3)

Solving (c): P(-1,-2) \to Q(-2,-2)

This means that:

(x,y) \to (x-1,y)

So, we have:

A = (-1,1)

A' = (-1-1,1)

A' = (-2,1)

B  = (3,3)

B'= (3-1,3)

B'= (2,3)

C =(4,-2)

C'= (4-1,-2)

C'= (3,-2)

Mathematics
Step-by-step answer
P Answered by Master

See explanation

Step-by-step explanation:

Given

A = (-1,1)

B  = (3,3)

C =(4,-2)

Solving (a): P(0,0) \to Q(1,3)

This means that:

(x,y) \to (x+1,y+2)

So, we have:

A = (-1,1)

A' = (-1 + 1,1+2)

A' = (0,3)

B  = (3,3)

B'= (3 + 1,3+2)

B'= (4,5)

C =(4,-2)

C' = (4+1,-2+1)

C' = (5,-1)

Solving (b): P(0,-1) \to Q(4,-2)

This means that:

(x,y) \to (x+4,y-1)

So, we have:

A = (-1,1)

A' = (-1+4,1-1)

A' = (3,0)

B  = (3,3)

B'= (3+4,3-1)

B'= (7,2)

C =(4,-2)

C' = (4+4,-2-1)

C' = (8,-3)

Solving (c): P(-1,-2) \to Q(-2,-2)

This means that:

(x,y) \to (x-1,y)

So, we have:

A = (-1,1)

A' = (-1-1,1)

A' = (-2,1)

B  = (3,3)

B'= (3-1,3)

B'= (2,3)

C =(4,-2)

C'= (4-1,-2)

C'= (3,-2)

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