Question

question 1 the image of the point (2, - 3) under a translation is (-1, 1). find the coordinates of the image of the point (5, 6) under the same translation.

Explanation:

Step1: Find the translation rule

If the image of the point $(2,- 3)$ under a translation is $(-1,1)$, then the translation rule is found by subtracting the original - point coordinates from the image - point coordinates. Let the translation be $(x,y)\to(x + a,y + b)$. For the $x$ - coordinate: $-1-2=a$, so $a=-3$. For the $y$ - coordinate: $1-( - 3)=b$, so $b = 4$. The translation rule is $(x,y)\to(x-3,y + 4)$.

Step2: Apply the translation rule to the new point

We want to find the image of the point $(5,6)$ under the same translation. For the $x$ - coordinate of the new image: $x=5-3 = 2$. For the $y$ - coordinate of the new image: $y=6 + 4=10$.

Answer:

$(2,10)$