Question

write the coordinates of the vertices after a translation 6 units left and 1 unit up.
s((
t(
u(

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( S \), \( T \), and \( U \) from the graph.

• \( S \): Looking at the grid, \( S \) is at \( (-1, -3) \) (wait, no, let's check again. Wait, the x - axis: U is at \( x=-1 \)? Wait, the grid lines: Let's see, U is at \( x = - 1\)? Wait, no, the x - coordinate of U: the vertical line through U is at \( x=-1 \)? Wait, no, the grid has x from - 10 to 10. Let's check the points:

Wait, \( S \): Let's see, the y - coordinate of S is - 3 (since it's 3 units below the x - axis), and x - coordinate: looking at the horizontal line, S is at \( x=-1 \)? Wait, no, maybe I made a mistake. Wait, the original coordinates:

Looking at the graph:

• \( S \): The point S is at \( ( - 1, - 3) \)? Wait, no, let's check the grid. Wait, the x - axis: each grid square is 1 unit. Let's see, U is at \( ( - 1, - 1) \)? Wait, no, the y - coordinate of U: U is at \( y=-1 \) (since it's 1 unit below the x - axis), x - coordinate: \( x=-1 \). Then S is directly below U, so S has the same x - coordinate as U, and y - coordinate is \( - 3 \) (since it's 2 units below U). So \( S=(-1,-3) \), \( U = (-1,-1) \), and \( T=(8,-3) \) (since T is at x = 8, y=-3).

Step2: Apply translation rule

The translation is 6 units left (which means subtract 6 from the x - coordinate) and 1 unit up (which means add 1 to the y - coordinate). The translation rule for a point \( (x,y) \) is \( (x - 6,y + 1) \).

For point \( S(-1,-3) \):

• New x - coordinate: \( -1-6=-7 \)
• New y - coordinate: \( -3 + 1=-2 \)

So \( S'=(-7,-2) \)

For point \( T(8,-3) \):

• New x - coordinate: \( 8-6 = 2 \)
• New y - coordinate: \( -3+1=-2 \)

So \( T'=(2,-2) \)

For point \( U(-1,-1) \):

• New x - coordinate: \( -1-6=-7 \)
• New y - coordinate: \( -1 + 1=0 \)

So \( U'=(-7,0) \)

Answer:

\( S'(-7, - 2) \), \( T'(2, - 2) \), \( U'(-7, 0) \)