Question

point p(2, 3) is the image of point p(2, 3) under a translation. select is the image of (6, - 2) under the same translation?
a (11, - 1)
b (13, - 3)
c (9, - 9)
d (3, 5)

Explanation:

Step1: Find translation rule

Let the translation be $(x,y)\to(x + a,y + b)$. Given $P(2,3)$ is mapped to $P'(7,-1)$. So, $2 + a=7$ and $3 + b=-1$. Solving $2 + a=7$ gives $a = 5$, and solving $3 + b=-1$ gives $b=-4$. The translation rule is $(x,y)\to(x + 5,y-4)$.

Step2: Apply translation to $(6,-2)$

For the point $(6,-2)$, using the rule $(x,y)\to(x + 5,y - 4)$, we substitute $x = 6$ and $y=-2$. The new $x$-coordinate is $6+5 = 11$, and the new $y$-coordinate is $-2-4=-6$.

Answer:

$(11,-6)$