Question

directions: follow all four instructions below and place explanation at the bottom of each instruction.
translate a by the directed line segment from (0,0) to (0,2). place the red dot below to show your answer.
explanation:
translate a by the directed line segment from (0,0) to (-4,0). place the yellow dot below to show your answer.
explanation:
reflect a across the x - axis. place the blue dot below to show your answer.
explanation:
rotate a 180 degrees clockwise using the origin as a center. place the green dot below to show your answer.
explanation:
use:

Explanation:

Step1: Translation (0,0) to (0,2)

To translate a point \(A(x,y)\) by the directed - line segment from \((0,0)\) to \((0,2)\), we add the components of the vector \(\vec{v}=(0,2)\) to the coordinates of \(A\). If \(A=(x,y)\), the new point \(A_1=(x + 0,y + 2)=(x,y + 2)\).

Step2: Translation (0,0) to (-4,0)

To translate a point \(A(x,y)\) by the directed - line segment from \((0,0)\) to \((-4,0)\), we add the components of the vector \(\vec{u}=(-4,0)\) to the coordinates of \(A\). If \(A=(x,y)\), the new point \(A_2=(x-4,y + 0)=(x - 4,y)\).

Step3: Reflection across the x - axis

To reflect a point \(A(x,y)\) across the \(x\) - axis, we change the sign of the \(y\) - coordinate. The new point \(A_3=(x,-y)\).

Step4: 180 - degree clockwise rotation about the origin

To rotate a point \(A(x,y)\) 180 degrees clockwise about the origin, we change the signs of both coordinates. The new point \(A_4=(-x,-y)\).

Answer:

For the first translation: If \(A=(x,y)\), the new point is \((x,y + 2)\); for the second translation: the new point is \((x - 4,y)\); for the reflection across the \(x\) - axis: the new point is \((x,-y)\); for the 180 - degree clockwise rotation about the origin: the new point is \((-x,-y)\)