Question

triangle abc has coordinates a(2,0), b(-1,5), and c(4,3). determine the coordinates of the vertices of the image after a rotation 90° counterclockwise about the origin.
o a) a(0,2), b(-5,-1), and c(-3,4)
o b) a(2,0), b(-1,-5), and c(4,-3)
o c) a(2,2), b(-1,7), and c(4,5)
o d) a(-2,0), b(1,-5), and c(-4,-3)

Explanation:

Step1: Recall the rotation formula

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

Step2: Apply the formula to point \(A(2,0)\)

For \(A(2,0)\), \(x = 2\) and \(y=0\). Using the formula \((x',y')=(-y,x)\), we get \(A'(0,2)\) (since \(-y=-0 = 0\) and \(x = 2\)).

Step3: Apply the formula to point \(B(-1,5)\)

For \(B(-1,5)\), \(x=-1\) and \(y = 5\). Using the formula \((x',y')=(-y,x)\), we get \(B'(-5,-1)\) (since \(-y=-5\) and \(x=-1\)).

Step4: Apply the formula to point \(C(4,3)\)

For \(C(4,3)\), \(x = 4\) and \(y = 3\). Using the formula \((x',y')=(-y,x)\), we get \(C'(-3,4)\) (since \(-y=-3\) and \(x = 4\)).

Answer:

A. \(A'(0,2)\), \(B'(-5,-1)\), and \(C'(-3,4)\)