Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.
j((□, □))
k((□, □))
l((□, □))

Explanation:

Step1: Identify original coordinates

First, find the coordinates of \( J \), \( K \), and \( L \) from the graph.

• \( J \) is at \( (-5, -8) \) (since it's 5 units left on x - axis and 8 units down on y - axis).
• \( K \) is at \( (-5, -1) \) (5 units left on x - axis and 1 unit down on y - axis).
• \( L \) is at \( (0, -10) \) (on y - axis, 10 units down).

Step2: Apply 180° rotation rule

The rule for a 180° counterclockwise (or clockwise) rotation around the origin is \( (x,y)\to(-x,-y) \).

• For \( J(-5, -8) \):

Apply the rule: \( x=-5\to -(-5) = 5 \), \( y = -8\to-(-8)=8 \). So \( J'=(5,8) \).

• For \( K(-5, -1) \):

Apply the rule: \( x=-5\to -(-5) = 5 \), \( y=-1\to-(-1) = 1 \). So \( K'=(5,1) \).

• For \( L(0, -10) \):

Apply the rule: \( x = 0\to-0=0 \), \( y=-10\to-(-10)=10 \). So \( L'=(0,10) \).

Answer:

\( J'(5, 8) \), \( K'(5, 1) \), \( L'(0, 10) \)