Question

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

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( J \): Looking at the graph, \( J \) is at \( (-9, -7) \) (since it's 9 units left on the x - axis and 7 units down on the y - axis).
• \( K \): \( K \) is at \( (-9, 0) \) (9 units left on x, 0 on y).
• \( L \): \( L \) is at \( (-4, 1) \) (4 units left on x, 1 unit up on y).
• \( M \): \( M \) is at \( (-4, -6) \) (4 units left on x, 6 units down on y).

Step2: Apply translation (4 units up)

A translation of 4 units up means we add 4 to the y - coordinate of each vertex (the x - coordinate remains the same). The rule for a translation \( (x,y)\to(x,y + 4) \).

• For \( J(-9,-7) \):

New y - coordinate: \( -7+4=-3 \). So \( J'(-9,-3) \).

• For \( K(-9,0) \):

New y - coordinate: \( 0 + 4=4 \). So \( K'(-9,4) \).

• For \( L(-4,1) \):

New y - coordinate: \( 1+4 = 5 \). So \( L'(-4,5) \).

• For \( M(-4,-6) \):

New y - coordinate: \( -6 + 4=-2 \). So \( M'(-4,-2) \).

Answer:

\( J'(-9, -3) \), \( K'(-9, 4) \), \( L'(-4, 5) \), \( M'(-4, -2) \)