Question

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

1. a translation 1 unit to the left and 2 units down;

ii. a reflection in the ( y )-axis; and
iii. a ( 90^{circ} ) counterclockwise rotation about the origin

Explanation:

Step1: Translation

For a translation \(1\) unit to the left (\(x\)-coordinate decreases by \(1\)) and \(2\) units down (\(y\)-coordinate decreases by \(2\)), if the original point is \(B(3,2)\), the new coordinates after translation are \((3 - 1,2-2)=(2,0)\).

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

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

Step3: \(90^{\circ}\) counter - clockwise rotation about the origin

The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-y,x)\). For the point \((-2,0)\), substituting \(x=-2\) and \(y = 0\) into the rule, we get \((-0,-2)=(0,-2)\)

Answer:

\(H\)