Question

a changes the size of a shape by a specific scale factor while maintaining its proportions. translating a point (x, y) to the right by 4 units and up by 3 units will move it to. rotating a point (a, b) 90 degrees clockwise around the origin changes its coordinates to.

Explanation:

1. A dilation changes the size of a shape by a specific scale - factor while maintaining its proportions. This is a key concept in geometry where shapes are resized.
2. When translating a point $(x,y)$ to the right by 4 units and up by 3 units, we add 4 to the $x$ - coordinate and 3 to the $y$ - coordinate. So the new point is $(x + 4,y+3)$.
3. When rotating a point $(a,b)$ 90 degrees clockwise around the origin, the new coordinates are $(b,-a)$. This is based on the rotation rules in the coordinate - plane.

Answer:

1. Dilation
2. $(x + 4,y + 3)$
3. $(b,-a)$