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
c
h
d
e

Explanation:

Step1: Translation

The rule for a translation \(2\) units to the left (\(x - 2\)) and \(5\) units up (\(y+5\)) is \((x,y)\to(x - 2,y + 5)\).
For the point \(A(2,-3)\), we substitute \(x = 2\) and \(y=-3\) into the rule:
\((2-2,-3 + 5)=(0,2)\)

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

The rule for a reflection in the \(x -\)axis is \((x,y)\to(x,-y)\).
For the point \((0,2)\), we substitute \(x = 0\) and \(y = 2\) into the rule: \((0,-2)\)

Step3: \(180^{\circ}\) clockwise rotation about the origin

The rule for a \(180^{\circ}\) clockwise rotation about the origin is \((x,y)\to(-x,-y)\).
For the point \((0,-2)\), we substitute \(x = 0\) and \(y=-2\) into the rule: \((0,2)\)

Looking at the graph, point \(C\) has coordinates \((0,2)\)

Answer:

\(C\)