Question

graph the image of δklm after a translation 10 units right and 5 units up.

Explanation:

Step1: Find coordinates of K, L, M

From the graph:

• \( K(-3, -3) \) (since it's 3 units left of y-axis, 3 units down of x-axis)
• \( L(-2, 5) \) (2 units left of y-axis, 5 units up of x-axis)
• \( M(-4, -1) \) (4 units left of y-axis, 1 unit down of x-axis)

Step2: Apply translation (10 right, 5 up)

Translation rule: \( (x, y) \to (x + 10, y + 5) \)

• For \( K(-3, -3) \): \( (-3 + 10, -3 + 5) = (7, 2) \)
• For \( L(-2, 5) \): \( (-2 + 10, 5 + 5) = (8, 10) \)
• For \( M(-4, -1) \): \( (-4 + 10, -1 + 5) = (6, 4) \)

Step3: Plot new points

Plot \( K'(7, 2) \), \( L'(8, 10) \), \( M'(6, 4) \) and connect them to form the translated triangle.

Answer:

The translated triangle \( \triangle K'L'M' \) has vertices at \( (7, 2) \), \( (8, 10) \), and \( (6, 4) \) (graph by plotting these points).