Question

graph the image of square klmn after a translation 6 units left and 4 units up.

Explanation:

Step1: Find coordinates of K, L, M, N

From the graph:

• \( K(5, -5) \)
• \( L(7, -5) \)
• \( M(7, -3) \)
• \( N(5, -3) \)

Step2: Apply translation (left 6, up 4)

Translation rule: \((x, y) \to (x - 6, y + 4)\)

• For \( K(5, -5) \): \( (5 - 6, -5 + 4) = (-1, -1) \)
• For \( L(7, -5) \): \( (7 - 6, -5 + 4) = (1, -1) \)
• For \( M(7, -3) \): \( (7 - 6, -3 + 4) = (1, 1) \)
• For \( N(5, -3) \): \( (5 - 6, -3 + 4) = (-1, 1) \)

Step3: Plot the new points

Plot \( K'(-1, -1) \), \( L'(1, -1) \), \( M'(1, 1) \), \( N'(-1, 1) \) and connect them to form the translated square.

Answer:

The translated square has vertices at \( K'(-1, -1) \), \( L'(1, -1) \), \( M'(1, 1) \), \( N'(-1, 1) \). (Graphing these points on the coordinate plane as described completes the task.)