"A dilation centered at the origin with scale factor to 1/2 from the origin" means that we must join O to all the vertices of the triangle, and make the distances 1/2 of the original triangle. This is shown clearly in the picture.
The coordinates of the new triangle are A'(0,4), B'(1,-1), C'(-1,-1).
<span>
The relationship between corresponding sides in terms of their lengths:
The sides of the dilated triangle are half the length of the first triangle.
</span><span>The relationship between corresponding sides in terms of their orientations.
The two triangles have the same orientation.
</span><span>The relationship between corresponding angles in terms of their measures.
The two triangles have congruent corresponding angles.</span>
The coordinates of the new triangle are A'(0,4), B'(1,-1), C'(-1,-1).
<span>
The relationship between corresponding sides in terms of their lengths:
The sides of the dilated triangle are half the length of the first triangle.
</span><span>The relationship between corresponding sides in terms of their orientations.
The two triangles have the same orientation.
</span><span>The relationship between corresponding angles in terms of their measures.
The two triangles have congruent corresponding angles.</span>