Question

write the coordinates of the vertices after a translation 2 units down.

Explanation:

Step1: Identify original coordinates

From the graph:

• \( J \): \( (0, 3) \) (wait, no, looking at the grid, \( J \) is at \( (0, 3) \)? Wait, the y-axis: let's check again. Wait, the grid lines: \( J \) is at \( (0, 3) \)? Wait, no, the blue dot for \( J \) is at y=3? Wait, no, the original coordinates:
• \( J \): \( (0, 3) \)? Wait, no, looking at the graph, \( J \) is at (0, 3)? Wait, no, the vertical axis (y-axis) has 2, 4, 6, 8, 10. So each grid line is 1 unit. So:
• \( L \): (0, 5) (since it's at y=5, x=0)
• \( K \): (1, 4) (x=1, y=4)
• \( J \): (0, 3) (x=0, y=3)
• \( M \): (-4, 4) (x=-4, y=4) Wait, no, the blue dot for \( M \): let's count the x-coordinate. From the y-axis (x=0), moving left 4 units: x=-4, y=4.

Wait, maybe I misread. Let's re-express:

Looking at the graph:

• \( L \): (0, 5) (x=0, y=5)
• \( K \): (1, 4) (x=1, y=4)
• \( J \): (0, 3) (x=0, y=3)
• \( M \): (-4, 4) (x=-4, y=4)

Step2: Apply translation 2 units down

Translation 2 units down means subtract 2 from the y-coordinate of each vertex.

For \( L \): (0, 5 - 2) = (0, 3)

For \( K \): (1, 4 - 2) = (1, 2)

For \( J \): (0, 3 - 2) = (0, 1)

For \( M \): (-4, 4 - 2) = (-4, 2)

Wait, maybe my original coordinates were wrong. Let's check again. Let's look at the grid:

• \( L \): on the y-axis, at y=5 (since between 4 and 6, so y=5), x=0: (0,5)
• \( K \): x=1, y=4: (1,4)
• \( J \): x=0, y=3: (0,3)
• \( M \): x=-4 (since 4 units left of y-axis), y=4: (-4,4)

Yes. So translating 2 units down: y-coordinate decreases by 2.

So:

• \( L \): (0, 5 - 2) = (0, 3)
• \( K \): (1, 4 - 2) = (1, 2)
• \( J \): (0, 3 - 2) = (0, 1)
• \( M \): (-4, 4 - 2) = (-4, 2)

Wait, but maybe the original coordinates are different. Wait, the blue dot for \( M \): let's count the x-coordinate. From the y-axis (x=0), moving left 4 units: x=-4, y=4. Correct.

So after translation 2 units down (subtract 2 from y):

• \( L \): (0, 5 - 2) = (0, 3)
• \( K \): (1, 4 - 2) = (1, 2)
• \( J \): (0, 3 - 2) = (0, 1)
• \( M \): (-4, 4 - 2) = (-4, 2)

Answer:

• \( L' \): \( (0, 3) \)
• \( K' \): \( (1, 2) \)
• \( J' \): \( (0, 1) \)
• \( M' \): \( (-4, 2) \)