Question

describe the translation of the point to its image. (4, -2) → (-1, -7) (x,y) → describe the translation of the point to its image. (-3, 2) → (6, 6) (x,y) → describe the translation of the point to its image. (4, 3) → (-7, 0) (x,y) →

Explanation:

Step1: Find x - translation for first pair

For the point $(4, - 2)\to(-1,-7)$, find the change in x - coordinate. $\Delta x=-1 - 4=-5$.

Step2: Find y - translation for first pair

Find the change in y - coordinate. $\Delta y=-7-( - 2)=-5$. So the translation is $(x,y)\to(x - 5,y - 5)$.

Step3: Find x - translation for second pair

For the point $(-3,2)\to(6,6)$, $\Delta x=6-( - 3)=9$.

Step4: Find y - translation for second pair

$\Delta y=6 - 2 = 4$. So the translation is $(x,y)\to(x + 9,y + 4)$.

Step5: Find x - translation for third pair

For the point $(4,3)\to(-7,0)$, $\Delta x=-7 - 4=-11$.

Step6: Find y - translation for third pair

$\Delta y=0 - 3=-3$. So the translation is $(x,y)\to(x - 11,y - 3)$.

Answer:

$(x,y)\to(x - 5,y - 5)$
$(x,y)\to(x + 9,y + 4)$
$(x,y)\to(x - 11,y - 3)$