Question

write the coordinates of the vertices after a translation 4 units down.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex. From the graph:

• \( R \): \( (-8, -4) \)
• \( S \): \( (-8, -3) \) (Wait, no, looking at the grid, S is at (-8, -3)? Wait, no, let's check again. Wait, R is at (-8, -4), S is at (-8, -3)? Wait, no, the y-axis: each grid is 1 unit. Let's re-express:

Wait, the points:

• \( R \): x=-8, y=-4 (since it's on the -8 x and -4 y)
• \( S \): x=-8, y=-3? Wait, no, looking at the graph, S is above R. Wait, R is at (-8, -4), S is at (-8, -3)? Wait, no, maybe I misread. Wait, the vertical line at x=-8: R is at y=-4, S is at y=-3? Wait, no, the graph shows R at (-8, -4), S at (-8, -3)? Wait, no, let's check T and U. T is at (1, 5)? Wait, no, x=1? Wait, the grid: each square is 1 unit. Let's see: T is at (1, 5)? Wait, no, the x-coordinate for T: from the y-axis (x=0), moving 1 unit right? Wait, no, the graph: T is at (1, 5)? Wait, no, looking at the grid, T is at (1, 5)? Wait, no, the x-axis: the point T is at x=1, y=5? Wait, no, the vertical line at x=1? Wait, no, the grid lines: each vertical line is 1 unit. So T is at (1, 5)? Wait, no, the original coordinates:

Wait, let's list each vertex:

• \( R \): x = -8, y = -4 (since it's on the -8 column and -4 row)
• \( S \): x = -8, y = -3 (above R, 1 unit up)
• \( T \): x = 1, y = 5 (right of y-axis, 1 unit, y=5)
• \( U \): x = 1, y = 1 (below T, 4 units down? Wait, no, U is at (1, 1)? Wait, no, looking at the graph, U is at (1, 1)? Wait, no, the original U: from the graph, U is at (1, 1)? Wait, no, the y-coordinate for U: between 0 and 2? Wait, no, the grid: U is at (1, 1)? Wait, maybe I made a mistake. Let's re-express:

Wait, the original coordinates:

• \( R \): (-8, -4)
• \( S \): (-8, -3)
• \( T \): (1, 5)
• \( U \): (1, 1)

Wait, no, looking at the graph, T is at (1, 5)? Wait, the y-axis: 0, 1, 2, 3, 4, 5, 6... So T is at (1, 5), U is at (1, 1). S is at (-8, -3), R is at (-8, -4).

Step2: Apply translation (4 units down)

Translation 4 units down means subtract 4 from the y-coordinate (since down is negative y direction). The translation rule is \((x, y) \to (x, y - 4)\).

• For \( R(-8, -4) \):

New y-coordinate: \(-4 - 4 = -8\), so \( R'(-8, -8) \)

• For \( S(-8, -3) \):

New y-coordinate: \(-3 - 4 = -7\), so \( S'(-8, -7) \)

• For \( T(1, 5) \):

New y-coordinate: \(5 - 4 = 1\), so \( T'(1, 1) \)

• For \( U(1, 1) \):

New y-coordinate: \(1 - 4 = -3\), so \( U'(1, -3) \)

Wait, but maybe I misread the original coordinates. Let's check again. Wait, maybe T is at (1, 5)? Wait, no, the graph: T is at (1, 5)? Wait, the vertical line at x=1, y=5. U is at (1, 1). S is at (-8, -3), R is at (-8, -4).

Wait, maybe the original coordinates are:

• \( R \): (-8, -4)
• \( S \): (-8, -3)
• \( T \): (1, 5)
• \( U \): (1, 1)

Then, translating 4 units down: subtract 4 from y.

So:

• \( R' \): (-8, -4 - 4) = (-8, -8)
• \( S' \): (-8, -3 - 4) = (-8, -7)
• \( T' \): (1, 5 - 4) = (1, 1)
• \( U' \): (1, 1 - 4) = (1, -3)

Wait, but maybe the original T is at (1, 5)? Let's confirm the grid. Each square is 1 unit. So from y=0, up is positive, down is negative. So T is at (1, 5), U at (1, 1), S at (-8, -3), R at (-8, -4).

Yes, that makes sense. So after translating 4 units down, each y-coordinate decreases by 4.

Answer:

The coordinates after translation 4 units down are:
\( R'(-8, -8) \), \( S'(-8, -7) \), \( T'(1, 1) \), \( U'(1, -3) \)