Question

translations
determine the coordinates of the image following each given translation.
① triangle abc with coordinates a(2, 4), b(3, 6), and c(5, 1) is translated 4 units horizontally.
② parallelogram defg with coordinates d(0, 2), e(1, 5), f(6, 5), and g(5, 2) is translated -7 units horizontally.
6 fill in the blank 2 points
a.
a ( type your answer... type your answer... )
b ( type your answer... type your answer... )
c ( type your answer... type your answer... )

Explanation:

Step1: Recall translation rule for horizontal shift

For a horizontal translation of $h$ units, if $h>0$ we move right and if $h < 0$ we move left. The rule for a point $(x,y)$ is $(x + h,y)$.

Step2: Translate point A

Given $A(2,4)$ and $h = 4$ (4 units horizontally). Using the rule $(x+h,y)$, we have $x=2$, $y = 4$ and $h = 4$. So $A'=(2 + 4,4)=(6,4)$.

Step3: Translate point B

Given $B(3,6)$ and $h = 4$. Using the rule $(x + h,y)$, we substitute $x = 3$, $y=6$ and $h = 4$. So $B'=(3 + 4,6)=(7,6)$.

Step4: Translate point C

Given $C(5,1)$ and $h = 4$. Using the rule $(x + h,y)$, we substitute $x = 5$, $y = 1$ and $h=4$. So $C'=(5 + 4,1)=(9,1)$.

Answer:

$A'(6,4)$
$B'(7,6)$
$C'(9,1)$