Question

write the coordinates of the vertices after a translation 2 units left.
k(□, □)
l(□, □)
m(□, □)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( K \), \( L \), and \( M \) from the graph.

• \( K \) is at \( (-4, -5) \) (since it's 4 units left on the x - axis and 5 units down on the y - axis).
• \( L \) is at \( (3, -5) \) (3 units right on the x - axis and 5 units down on the y - axis).
• \( M \) is at \( (-2, 2) \) (2 units left on the x - axis and 2 units up on the y - axis).

Step2: Apply translation rule

A translation 2 units left means we subtract 2 from the x - coordinate of each point (the y - coordinate remains the same). The translation rule for a point \( (x,y) \) translated \( h \) units left is \( (x - h,y) \), here \( h = 2 \).

• For \( K(-4,-5) \):

New x - coordinate: \( - 4-2=-6 \), y - coordinate remains \( - 5 \). So \( K'(-6,-5) \).

• For \( L(3,-5) \):

New x - coordinate: \( 3 - 2 = 1 \), y - coordinate remains \( - 5 \). So \( L'(1,-5) \).

• For \( M(-2,2) \):

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

Answer:

\( K'(-6, -5) \)
\( L'(1, -5) \)
\( M'(-4, 2) \)