Question

1. rectangle wxyz with vertices w(-3,-4), x(0,-5), y(-2,-11),

and z(-5,-10); 180° rotation about point x.

w (__,__)
x (__,__)
y (__,__)
z (__,__)

1. triangle pqr with vertices p(-13,-3), q(-7,3), and r(-6,-2);

90° clockwise rotation about point r

Explanation:

Step1: Translate the point

To rotate a point \((x,y)\) \(180^{\circ}\) about a point \((a,b)\), we use the formula \((2a - x,2b - y)\).
For point \(W(-3,-4)\) and \(X(0,-5)\):
\(x=-3,y = - 4,a = 0,b=-5\)
\(W'(2\times0-(-3),2\times(-5)-(-4))=(3,-6)\)

Step2: For point \(X\)

Since we are rotating about \(X\), \(X'(0,-5)\) (a point rotated \(180^{\circ}\) about itself remains the same)

Step3: For point \(Y(-2,-11)\)

\(x=-2,y=-11,a = 0,b=-5\)
\(Y'(2\times0-(-2),2\times(-5)-(-11))=(2,1)\)

Step4: For point \(Z(-5,-10)\)

\(x=-5,y=-10,a = 0,b=-5\)
\(Z'(2\times0-(-5),2\times(-5)-(-10))=(5,0)\)

Answer:

\(W'(3,-6)\)
\(X'(0,-5)\)
\(Y'(2,1)\)
\(Z'(5,0)\)