Question

what is the image of point ( a(2,-3) ) after these three transformations?

1. a translation 2 units to the left and 5 units up;

ii. a reflection in the ( x )-axis; and
iii. a ( 180^{circ} ) clockwise rotation about the origin

Explanation:

Step1: Translation

For a translation \(2\) units to the left (\(x - 2\)) and \(5\) units up (\(y+5\)), if the original point is \((x,y)=(2,-3)\), then after translation, the new coordinates are \((2 - 2,-3 + 5)=(0,2)\).

Step2: Reflection in the \(x -\)axis

The rule for reflection in the \(x -\)axis is \((x,y)\to(x,-y)\). So, for the point \((0,2)\), after reflection, it becomes \((0,- 2)\).

Step3: \(180^{\circ}\) clock - wise rotation about the origin

The rule for a \(180^{\circ}\) clock - wise (or counter - wise) rotation about the origin is \((x,y)\to(-x,-y)\). For the point \((0,-2)\), after rotation, it becomes \((0,2)\).

Answer:

\(G\)