Question

question 12.
right triangle ( abc ) is shown below.
if triangle ( abc ) is rotated ( 90^{circ} ) clockwise around the origin, what are the new coordinates for vertex ( a )?
a. ( (3,-2) )
b. ( (2,-3) )
c. ( (3,2) )
d. ( (2,3) )

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) clockwise around the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(y,-x)\).

Step2: Apply the rule to point \(A(-2,3)\)

Here \(x = - 2\) and \(y = 3\). Substitute into the formula: \(x'=3\) and \(y'=-(-2)=2\).

Answer:

A. \((3, - 2)\)