Question

which are the coordinates of point ( b(4,3) ) after it is rotated ( 180^{circ} ) counterclockwise about the origin?
( (3,4) )
( (4,-3) )
( (-4,-3) )
( (-3,-4) )

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(-x,-y)\).

Step2: Apply the rule to point \(B(4,3)\)

Here \(x = 4\) and \(y=3\). Using the formula \((x',y')=(-x,-y)\), we substitute \(x = 4\) and \(y = 3\) into it.
For the \(x\) - coordinate: \(x'=-4\)
For the \(y\) - coordinate: \(y'=-3\)

Answer:

\((-4,-3)\)