Question

es 3 - 5 coordinate geometry find the coordinates of the figure with the given coordinates after the transformation on the plane. then graph the preimage and image. 10. a(3, 9), b(3, 7), c(7, 7); translation along the vector ⟨0, - 4⟩ 11. m(-7, -1), p(-7, -7), r(-1, -4); reflection in the y - axis 12. x(-5, -4), y(-2, 0), z(-2, -4); rotation by 270° counterclockwise 13. a(2, 2), b(4, 7), c(6, 2); reflection in the x - axis

Explanation:

Step1: Recall translation rule

For a translation along the vector $\langle a,b
angle$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x + a,y + b)$. Here $a = 0$ and $b=-4$.

Step2: Translate point A

For point $A(3,9)$, $x = 3,y = 9$. Then $x'=3+0 = 3$ and $y'=9+( - 4)=5$. So $A'(3,5)$.

Step3: Translate point B

For point $B(3,7)$, $x = 3,y = 7$. Then $x'=3 + 0=3$ and $y'=7+( - 4)=3$. So $B'(3,3)$.

Step4: Translate point C

For point $C(7,7)$, $x = 7,y = 7$. Then $x'=7+0 = 7$ and $y'=7+( - 4)=3$. So $C'(7,3)$.

Answer:

$A'(3,5),B'(3,3),C'(7,3)$