Question

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.

Explanation:

Step1: Recall translation rule for horizontal shift

For a horizontal translation of $h$ units, the $x$-coordinate of each point changes by $h$ and the $y$-coordinate remains the same.

For triangle ABC translated 4 units horizontally:

Let $(x,y)$ be the original - point and $(x',y')$ be the translated - point. The rule is $x'=x + 4$ and $y'=y$.

• For point $A(2,4)$:

$x'=2 + 4=6$, $y' = 4$. So the new coordinates of $A$ are $(6,4)$.

• For point $B(3,6)$:

$x'=3 + 4=7$, $y' = 6$. So the new coordinates of $B$ are $(7,6)$.

• For point $C(5,1)$:

$x'=5 + 4=9$, $y' = 1$. So the new coordinates of $C$ are $(9,1)$.

For parallelogram DEFG translated - 7 units horizontally:

The rule is $x'=x-7$ and $y'=y$.

• For point $D(0,2)$:

$x'=0 - 7=-7$, $y' = 2$. So the new coordinates of $D$ are $(-7,2)$.

• For point $E(1,5)$:

$x'=1 - 7=-6$, $y' = 5$. So the new coordinates of $E$ are $(-6,5)$.

• For point $F(6,5)$:

$x'=6 - 7=-1$, $y' = 5$. So the new coordinates of $F$ are $(-1,5)$.

• For point $G(5,2)$:

$x'=5 - 7=-2$, $y' = 2$. So the new coordinates of $G$ are $(-2,2)$.

Answer:

For triangle ABC: $A(6,4)$, $B(7,6)$, $C(9,1)$; For parallelogram DEFG: $D(-7,2)$, $E(-6,5)$, $F(-1,5)$, $G(-2,2)$