Question

Which rule describes the translation below ? In the picture

Answer 1

The translation rule which describes the given translation is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$.

Further explanation:

Translation is defined as the shifting of the curve in which each point on the curve is shifted in such a way that the shape and size of the curve remains unchanged but the position of each point is changed by a fixed distance.

In the given figure there are two right angle triangle as $S'T'U'$ and $STU$.

The coordinates of the right angle triangle $S'T'U'$ are $(-4,2),(-4,-2)$ and $(-1,-2)$ and the coordinates of the right angle triangle $STU$ are $(1,5),(1,1)$ and $(4,1)$.  

Consider that the triangle $STU$ is obtained after the translation of each point on the triangle $S'T'U'$.  

The coordinate of the point $S'$ in triangle $S'T'U'$ is $(-4,2)$.  

Step 1:  

Use the translation $(x,y)\rightarrow(x-5,y-3)$ for the point $S'$.  

$\fbox{\begin\\\(-4,2)\rightarrow(-4-5,2-3)=(-9,-1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-5,y-3)$ the coordinate of the point $S$ is $(-9,-1)$, but in the given figure the coordinate of the point $S$ is $(1,5)$.  

So, the translation $(x,y)\rightarrow(x-5,y-3)$ is incorrect.  

Step 2:  

Use the translation $(x,y)\rightarrow(x-3,y-5)$ for the point $S'$.  

$\fbox{\begin\\\(-4,2)\rightarrow(-4-3,2-5)=(-7,-3)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x-3,y-5)$ the coordinate of the point $S$ is $(-7,-3)$, but in the given figure the coordinate of the point $S$ is $(1,5)$.  

So, the translation $(x,y)\rightarrow(x-3,y-5)$ is incorrect.  

Step 3:  

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $S'$.  

$\fbox{\begin\\\(-4,2)\rightarrow(-4+5,2+3)=(1,5)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $S$ is $(1,5)$ which is correct as the coordinate for the point $S$ given in the figure is $(1,5)$.  

Step 4:  

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point $T'$.  

$\fbox{\begin\\\(-4,-2)\rightarrow(-4+5,-2+3)=(1,1)\\\end{minispace}}$  

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(1,1)$ which is correct as the coordinate for the point $T$ given in the figure is $(1,1)$.  

Step 5:  

Use the translation $(x,y)\rightarrow(x+5,y+3)$ for the point U’.  

$\fbox{\begin\\\ (-1,-2)\rightarrow(-1+5,-2+3)=(4,1)\\\end{minispace}}$

As per the translation $(x,y)\rightarrow(x+5,y+3)$ the coordinate of the point $T$ is $(4,1)$ which is correct as the coordinate for the point $U$ given in the figure is $(4,1)$.  

As per the above calculation it is concluded that the translation $(x,y)\rightarrow(x+5,y+3)$ is correct for the shifting of each point on the triangle $S'T'U'$ to each point on the triangle $STU$.

The translation of each point on the triangle $S'T'U'$ is shown in the image attached below.

Therefore, the correct translation rule for the shifting of the triangle $S'T'U'$ to the triangle $STU$ is $\fbox{\begin\\\math{(x,y)}\rightarrow(x+5,y-3)\\\end{minispace}}$  

Learn more:  

1. A problem to determine the range of a function brainly.com/question/3852778
2. A problem to determine the vertex of a curve brainly.com/question/1286775
3. A problem to convert degree into radians brainly.com/question/3161884  

Answer details:

Grade: Middle school

Subject: Mathematics  

Chapter: Coordinate geometry

Keywords: Translation, shifting, graph, geometry, coordinate geometry, coordinates, shifting of graph, triangle, right angle triangle, movement of curve, shifting of curve, translation of curve.

Answer 2

Answer:

(x, y)⇒(x-5, y-3)

Step-by-step explanation:

In the original figure we have the following vertices:

T(1, 1)

U(4, 1)

S(1, 5)

And in the translated figure we have the new vertices:

T'(-4, -2)

U'(-1, -2)

S'(-4, 2)

We can observe that from T to T 'the component in x was reduced by 5 and the component in y was reduced by 3:

(1 - 5, 1 - 3) = ( -4, -2) wich is T'

And the same goes for U and S

For U:

(4 - 5, 1 - 3) = (-1, -2) wich is U'

For S:

(1 - 5, 5 - 3) = (-4, 2) wich is S'

thus the rule for the translation is:

(x, y)⇒(x-5, y-3)