Question

write the new coordinates
write the coordinates obtained after the given translation

1. a(-5, 3), b(-3, 3), c(-2, 5), d(-5, 4)

8 units down and 7 units right
a: __, b: __
c: __, d: __

1. p(2, 1), q(4, 1), r(5, 3), s(2, 3)

2 units up and 5 units left
p: __, q: __
r: __, s: __

1. k(-5, -4), l(-2, -4), m(-2, -2), n(-5, -2)

4 units right and 3 units up
k: __, l: __
m: __, n: __

1. s(3, -5), t(4, -5), u(5, -3), v(2, -3)

7 units left and 6 units up
s: __, t: __
u: __, v: __

1. e(1, 2), f(3, 2), g(4, 4), h(2, 4)

5 units down and 1 unit left
e: __, f: __
g: __, h: __

1. j(-3, -5), k(-1, -5), l(-1, -3)

8 units up and 3 units right
j: __, k: __
l: ____

1. t(-5, 2), u(-1, 2), v(-2, 4), w(-4, 4)

6 units right and 6 units down
t: 1, -4, u: ____
v: __, w: __

1. a(0, 2), b(1, 4), c(0, 3), d(-1, 4)

4 units left and 1 unit down
a: __, b: __
c: __, d: __

Explanation:

Step1: Recall translation rule

For a point $(x,y)$, moving $a$ units right and $b$ units up gives $(x + a,y + b)$; moving $a$ units left and $b$ units down gives $(x - a,y - b)$.

Step2: Solve for 1)

For point $A(-5,3)$ moving 7 units right and 8 units down:
$x=-5 + 7=2$, $y=3-8=-5$, so $A'=(2,-5)$.
For point $B(-3,3)$ moving 7 units right and 8 units down:
$x=-3 + 7 = 4$, $y=3-8=-5$, so $B'=(4,-5)$.
For point $C(-2,5)$ moving 7 units right and 8 units down:
$x=-2+7 = 5$, $y=5 - 8=-3$, so $C'=(5,-3)$.
For point $D(-5,4)$ moving 7 units right and 8 units down:
$x=-5 + 7=2$, $y=4-8=-4$, so $D'=(2,-4)$.

Step3: Solve for 2)

For point $P(2,1)$ moving 5 units left and 2 units up:
$x=2-5=-3$, $y=1 + 2=3$, so $P'=(-3,3)$.
For point $Q(4,1)$ moving 5 units left and 2 units up:
$x=4-5=-1$, $y=1 + 2=3$, so $Q'=(-1,3)$.
For point $R(5,3)$ moving 5 units left and 2 units up:
$x=5-5 = 0$, $y=3+2=5$, so $R'=(0,5)$.
For point $S(2,3)$ moving 5 units left and 2 units up:
$x=2-5=-3$, $y=3 + 2=5$, so $S'=(-3,5)$.

Step4: Solve for 3)

For point $K(-5,-4)$ moving 4 units right and 3 units up:
$x=-5 + 4=-1$, $y=-4+3=-1$, so $K'=(-1,-1)$.
For point $L(-2,-4)$ moving 4 units right and 3 units up:
$x=-2 + 4=2$, $y=-4+3=-1$, so $L'=(2,-1)$.
For point $M(-2,-2)$ moving 4 units right and 3 units up:
$x=-2 + 4=2$, $y=-2+3=1$, so $M'=(2,1)$.
For point $N(-5,-2)$ moving 4 units right and 3 units up:
$x=-5 + 4=-1$, $y=-2+3=1$, so $N'=(-1,1)$.

Step5: Solve for 4)

For point $S(3,-5)$ moving 7 units left and 6 units up:
$x=3-7=-4$, $y=-5 + 6=1$, so $S'=(-4,1)$.
For point $T(4,-5)$ moving 7 units left and 6 units up:
$x=4-7=-3$, $y=-5 + 6=1$, so $T'=(-3,1)$.
For point $U(5,-3)$ moving 7 units left and 6 units up:
$x=5-7=-2$, $y=-3 + 6=3$, so $U'=(-2,3)$.
For point $V(2,-3)$ moving 7 units left and 6 units up:
$x=2-7=-5$, $y=-3 + 6=3$, so $V'=(-5,3)$.

Step6: Solve for 5)

For point $E(1,2)$ moving 1 unit left and 5 units down:
$x=1-1 = 0$, $y=2-5=-3$, so $E'=(0,-3)$.
For point $F(3,2)$ moving 1 unit left and 5 units down:
$x=3-1=2$, $y=2-5=-3$, so $F'=(2,-3)$.
For point $G(4,4)$ moving 1 unit left and 5 units down:
$x=4-1=3$, $y=4-5=-1$, so $G'=(3,-1)$.
For point $H(2,4)$ moving 1 unit left and 5 units down:
$x=2-1=1$, $y=4-5=-1$, so $H'=(1,-1)$.

Step7: Solve for 6)

For point $J(-3,-5)$ moving 3 units right and 8 units up:
$x=-3 + 3=0$, $y=-5+8=3$, so $J'=(0,3)$.
For point $K(-1,-5)$ moving 3 units right and 8 units up:
$x=-1 + 3=2$, $y=-5+8=3$, so $K'=(2,3)$.
For point $L(-1,-3)$ moving 3 units right and 8 units up:
$x=-1 + 3=2$, $y=-3+8=5$, so $L'=(2,5)$.

Step8: Solve for 7)

For point $T(-5,2)$ moving 6 units right and 6 units down:
$x=-5 + 6=1$, $y=2-6=-4$, so $T'=(1,-4)$.
For point $U(-1,2)$ moving 6 units right and 6 units down:
$x=-1 + 6=5$, $y=2-6=-4$, so $U'=(5,-4)$.
For point $V(-2,4)$ moving 6 units right and 6 units down:
$x=-2 + 6=4$, $y=4-6=-2$, so $V'=(4,-2)$.
For point $W(-4,4)$ moving 6 units right and 6 units down:
$x=-4 + 6=2$, $y=4-6=-2$, so $W'=(2,-2)$.

Step9: Solve for 8)

For point $A(0,2)$ moving 4 units left and 1 unit down:
$x=0-4=-4$, $y=2-1=1$, so $A'=(-4,1)$.
For point $B(1,4)$ moving 4 units left and 1 unit down:
$x=1-4=-3$, $y=4-1=3$, so $B'=(-3,3)$.
For point $C(0,3)$ moving 4 units left and 1 unit down:
$x=0-4=-4$, $y=3-1=2$, so $C'=(-4,2)$.
For point $D(-1,4)$ moving 4 units left and 1 unit down:
$x=-1-4=-5$, $y=4-1=3$, so $D'=(-5,3)$.

Answer:

1. $A':(2,-5)$, $B':(4,-5)$, $C':(5,-3)$, $D':(2,-4)$
2. $P':(-3,3)$, $Q':(-1,3)$, $R':(0,5)$, $S':(-3,5)$
3. $K':(-1,-1)$, $L':(2,-1)$, $M':(2,1)$, $N':(-1,1)$
4. $S':(-4,1)$, $T':(-3,1)$, $U':(-2,3)$, $V':(-5,3)$
5. $E':(0,-3)$, $F':(2,-3)$, $G':(3,-1)$, $H':(1,-1)$
6. $J':(0,3)$, $K':(2,3)$, $L':(2,5)$
7. $T':(1,-4)$, $U':(5,-4)$, $V':(4,-2)$, $W':(2,-2)$
8. $A':(-4,1)$, $B':(-3,3)$, $C':(-4,2)$, $D':(-5,3)$