Question

1. rotation 180° counterclockwise around the origin
2. translation 14 units right and 9 units down

Explanation:

First, identify the coordinates of the original triangle's vertices:

• Let the bottom-left blue vertex be $A(-4, -13)$
• Let the bottom-right blue vertex be $B(2, -13)$
• Let the top blue vertex be $C( -1, -7)$

Step1: Rotate 180° counterclockwise

A 180° rotation around the origin transforms a point $(x,y)$ to $(-x,-y)$.

• For $A(-4,-13)$: $A' = (4, 13)$
• For $B(2,-13)$: $B' = (-2, 13)$
• For $C(-1,-7)$: $C' = (1, 7)$

Step2: Translate 14 right, 9 down

A translation of $(+14, -9)$ adds 14 to the x-coordinate and subtracts 9 from the y-coordinate of each rotated point.

• For $A'(4,13)$: $A'' = 4+14, 13-9 = (18, 4)$
• For $B'(-2,13)$: $B'' = -2+14, 13-9 = (12, 4)$
• For $C'(1,7)$: $C'' = 1+14, 7-9 = (15, -2)$

Answer:

The final coordinates of the transformed triangle are:
$(18, 4)$, $(12, 4)$, $(15, -2)$
To graph this, plot these three points and connect them to form the image triangle.