Question

ΔCAR has coordinates C (2, 4), A (1, 1), and R (3, 0). A translation maps point C to C' (3, 2). Find the coordinates of A' and R' under this translation. (6 points) A' (4, −2); R' (2, −1) A' (−2, 2); R' (2, −2) A' (2, −1); R' (4, −2) A' (−1, 0); R' (−2, 2).

Answer 1

Answer:

$A'= (2,-1)$ and $R'=(4,-2)$ under this translation.

Step-by-step explanation:

A translation in $R^{2}$ is a mapping T from $R^{2}$ to $R^{2}$  defined by $T(x,y) = (x + v_1,y+v_2)$, where $v=(v_1,v_2)$ is a fixed vector in $R^{2}$.

From the problem we know that $T(2,4)=(3,2)$, so we need to find the values $v_1$ and $v_2$ such that  $T(2,4) = (2 + v_1,4+v_2)=(3,2)$, so $3=2 + v_1$ and $4+v_2=2$, thus $v_1=1$ and $v_2=2$.

Then $T(x,y) = (x + 1,y-2)$ and  

$T(1,1)=(1+1,1-2)=(2,-1)=A'$

$T(3,0)=(3+1,0-2)=(4,-2)=R'$

Therefore $A'= (2,-1)$ and $R'=(4,-2)$. The triangles CAR and C'Q'R' are shown in the figure below.