Question

solve the following questions. what are the coordinates of point s(5, - 3) after the translation (x, y) → (x + 2, y - 9)? point c(-6, -1) is the image of c(0, -1) after a translation. write the algebraic description of the translation. triangle bdf, a translation of △bdf, is shown on the coordinate plane. write the algebraic description for the translation. polygons wrtp and wrtpl are shown on the coordinate plane. what is the algebraic description of the transformation that maps wrtp to wrtpl? polygon btgdc was transformed to create polygon btgdc. which graph matches the transformation (x, y) → (x, y - 7)?

Explanation:

Step1: Find new x - coordinate for point S

Given the translation rule $(x,y)\to(x + 2,y-9)$ and the point $S(5,-3)$. For the x - coordinate, substitute $x = 5$ into $x+2$. So, $x'=5 + 2=7$.

Step2: Find new y - coordinate for point S

Substitute $y=-3$ into $y - 9$. So, $y'=-3-9=-12$.

Step3: Determine algebraic description for translation of C

Given $C(0,-1)$ and $C'(-6,-1)$. The change in x is $-6-0=-6$ and the change in y is $-1-(-1)=0$. So the algebraic description is $(x,y)\to(x - 6,y)$.

Step4: Analyze translation of triangles

For the translation of $\triangle BDF$ to $\triangle B'D'F'$, count the horizontal and vertical shifts. Suppose a vertex of $\triangle BDF$ is $(x_1,y_1)$ and its corresponding vertex in $\triangle B'D'F'$ is $(x_2,y_2)$. If we observe the shift, assume we find that the horizontal shift is $h$ and vertical shift is $k$. The algebraic description is $(x,y)\to(x + h,y + k)$.

Step5: Analyze translation of polygons

For polygons $WRTP$L and $W'R'T'P'L'$, find the change in x and y - coordinates of corresponding vertices. Let a vertex of $WRTP$L be $(x,y)$ and its corresponding vertex in $W'R'T'P'L'$ be $(x',y')$. Calculate $x'-x$ and $y'-y$ to get the translation rule $(x,y)\to(x+(x'-x),y+(y'-y))$.

Step6: Identify the correct graph for $(x,y)\to(x,y - 7)$

The translation $(x,y)\to(x,y - 7)$ means a vertical shift downwards by 7 units. We need to check which of the graphs A, B, C, D shows the polygon $BTGDC$ shifted down by 7 units.

Answer:

1. The coordinates of point S after translation are $(7,-12)$.
2. The algebraic description of the translation for point C is $(x,y)\to(x - 6,y)$.
3. (Answer for algebraic description of $\triangle BDF$ translation depends on actual shift values counted from the graph, assume we find it's $(x,y)\to(x+3,y - 2)$ for example).
4. (Answer for algebraic description of $WRTP$L to $W'R'T'P'L'$ translation depends on actual shift values counted from the graph, assume we find it's $(x,y)\to(x - 4,y+1)$ for example).
5. (Answer for the graph in question 6 depends on visual inspection, assume the correct answer is C if it shows the polygon shifted down by 7 units).