Question

lesson 5 practice problems

1. a. here are some points.

what are the coordinates of a, b, and c after a translation to the right by 4 units and up 1 unit? plot these points on the grid, and label them a, b and c.
b. here are some points.
what are the coordinates of d, e, and f after a reflection over the y - axis? plot these points on the grid, and label them d, e and f.

Explanation:

Step1: Recall translation rule

For a translation right by 4 units and up by 1 unit, the rule for a point $(x,y)$ is $(x + 4,y+1)$.

Step2: Find coordinates of $A'$, $B'$, $C'$ (assuming $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$ from the graph)

$A'=(x_1 + 4,y_1+1)$, $B'=(x_2 + 4,y_2+1)$, $C'=(x_3 + 4,y_3+1)$

Step3: Recall reflection rule over y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$.

Step4: Find coordinates of $D'$, $E'$, $F'$ (assuming $D(x_4,y_4)$, $E(x_5,y_5)$, $F(x_6,y_6)$ from the graph)

$D'=(-x_4,y_4)$, $E'=(-x_5,y_5)$, $F'=(-x_6,y_6)$

Since we don't have the exact coordinates of the points from the graph:
For translation:
If $A=(x_A,y_A)$, $A'=(x_A + 4,y_A+1)$; if $B=(x_B,y_B)$, $B'=(x_B + 4,y_B+1)$; if $C=(x_C,y_C)$, $C'=(x_C + 4,y_C+1)$
For reflection over y - axis:
If $D=(x_D,y_D)$, $D'=(-x_D,y_D)$; if $E=(x_E,y_E)$, $E'=(-x_E,y_E)$; if $F=(x_F,y_F)$, $F'=(-x_F,y_F)$

Answer:

The coordinates of $A'$, $B'$, $C'$ are found by adding 4 to the x - coordinate and 1 to the y - coordinate of $A$, $B$, $C$ respectively.
The coordinates of $D'$, $E'$, $F'$ are found by changing the sign of the x - coordinate of $D$, $E$, $F$ respectively while keeping the y - coordinate the same. To plot them, use the new - found coordinates on the given grids and label them accordingly.