Question

the graph shows triangles bcd and bcd.
which of the following transformations maps bcd onto bcd?
translation right 8 units
translation right 16 units
reflection across the x-axis
reflection across the y-axis
rotation $90^\circ$ clockwise around the origin
rotation $90^\circ$ counterclockwise around the origin
rotation $180^\circ$ around the origin

Explanation:

Step1: Identify coordinates of vertices

Coordinates:
$B(-6, -5)$, $C(-8, -7)$, $D(-4, -7)$
$B'(6, 5)$, $C'(8, 7)$, $D'(4, 7)$

Step2: Test transformation rules

For rotation $180^\circ$ around origin:
$(x,y) \to (-x,-y)$
Apply to $B(-6,-5)$: $-(-6), -(-5) = (6,5) = B'$
Apply to $C(-8,-7)$: $-(-8), -(-7) = (8,7) = C'$
Apply to $D(-4,-7)$: $-(-4), -(-7) = (4,7) = D'$

Step3: Verify match

All transformed points match $B'C'D'$.

Answer:

rotation $180^\circ$ around the origin