Question

1. graph the image of the figure using the rule given. then list the coordinates of the image (x,y)→(x + 2,y + 3). w ( , ) v ( , ) j ( , ) is this an example of rigid motion? why? 4. graph △abc with vertices a(-1,2), b(2,3), and c(4,-1). then graph the △abc with the translation (x,y)→(x - 3,y + 1). 5. translate the triangle so that c is at (4,-3). a) describe the translation. 6. the vertices of △mln are m(1,4), l(2,2) and n(5,6). if △mln is translated 8 units left and 3 units up to create △mln, what are the resulting coordinates of n? a. (-6,5) b. (-7,7) c. (13,-3) d. (-3,9) 7. describe the translation using coordinate - notation (x,y)→(x±a,y±b). is this rigid motion? 8. if the point (7,-4) translates to (0,-1), then (3,3) translates to ______. 9. what is the image of h(-2,1) after the translation that is defined by (x,y)→(x + 5,y + 2)? 10. what is the pre - image of g(6,-3) after the translation that is defined by (x,y)→(x - 3,y + 7)? 11. what is the image of b(-3,19) after the translation defined by (x,y)→(x - 8,y - 4)?

Explanation:

Step1: Recall translation rule

For a translation rule $(x,y)\to(x + a,y + b)$, we add $a$ to the $x$-coordinate and $b$ to the $y$-coordinate.

Step2: Solve problem 9

Given the point $H(-2,1)$ and the translation rule $(x,y)\to(x + 5,y + 2)$.
For the $x$-coordinate of the image: $x=-2+5 = 3$.
For the $y$-coordinate of the image: $y=1 + 2=3$. So the image of $H$ is $(3,3)$.

Answer:

$(3,3)$