Question

1. select all that apply: subtracting 2 units from the x and 1 unit from the y, does what? shifts the graph, 2 units to the right and 1 unit down. shifts the graph, 2 units to the left and 1 unit down. moves the center of rotation 2 units left and 1 unit down. the center of rotation (2, 1) becomes (0, 0)

Explanation:

• For a point \((x,y)\) in the coordinate plane, when we perform a transformation of subtracting \(a\) from the \(x -\)coordinate and \(b\) from the \(y -\)coordinate, the rule is \((x,y)\to(x - a,y - b)\).
• In a coordinate plane, subtracting from the \(x -\)coordinate moves the point horizontally. If we subtract from the \(x -\)coordinate (\(x\to x-2\)), the point moves to the left (since \(x\) values decrease as we move to the left). Subtracting from the \(y -\)coordinate (\(y\to y - 1\)) moves the point down (since \(y\) values decrease as we move down).
• If we consider a center of rotation \((x_0,y_0)=(2,1)\) and apply the transformation \((x_0,y_0)\to(x_0 - 2,y_0 - 1)=(2-2,1 - 1)=(0,0)\)

Answer:

B. Shifts the graph, 2 units to the left and 1 unit down.

C. Moves the center of rotation 2 units left and 1 unit down.

D. The center of rotation \((2,1)\) becomes \((0,0)\)