Question

animate rotation again
pre - image image
$(-7,-7)\to(7,7)$
$(-3,-6)\to(-6,3)$
$(-4,-4)\to(-4,4)$
$(-3,-2)\to(-2,3)$
$(-8,-4)\to(4,8)$
try values

Explanation:

Step1: Analyze the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the transformation rule is \((x,y)\to(-x,-y)\).

Step2: Apply the rule to each pre - image

• For the point \((-7,-7)\):

Using the rule \((x = - 7,y=-7)\), after rotation \(x'=-(-7) = 7\) and \(y'=-(-7)=7\).

• For the point \((-3,-6)\):

Using the rule \((x = - 3,y=-6)\), after rotation \(x'=-(-3) = 3\) and \(y'=-(-6)=6\). But wait, looking at the pattern of the given answers (maybe a mis - rule assumption). Wait, if we consider a rotation of \(90^{\circ}\) clockwise: the rule is \((x,y)\to(y,-x)\).
For \((-7,-7)\): \(x=-7,y = - 7\), then \(x'=-7,y' = 7\) (no). If we consider rotation about the \(y\) - axis: \((x,y)\to(-x,y)\) (no). If we consider rotation about the \(x\) - axis: \((x,y)\to(x,-y)\) (no). Wait, looking at the given pre - image \((-7,-7)\) to \((7,7)\), \((-3,-6)\) to \((6,3)\) (if we assume a reflection over \(y=-x\): the rule is \((x,y)\to(-y,-x)\)
For \((-7,-7)\): \(x=-7,y=-7\), then \(x'=-(-7)=7,y'=-(-7) = 7\)
For \((-3,-6)\): \(x=-3,y=-6\), then \(x'=-(-6)=6,y'=-(-3)=3\)
For \((-4,-4)\): \(x=-4,y=-4\), then \(x'=-(-4)=4,y'=-(-4)=4\)
For \((-3,-2)\): \(x=-3,y=-2\), then \(x'=-(-2)=2,y'=-(-3)=3\)
For \((-8,-4)\): \(x=-8,y=-4\), then \(x'=-(-4)=4,y'=-(-8)=8\)

Answer:

\((-7,-7)\to(7,7)\)
\((-3,-6)\to(6,3)\)
\((-4,-4)\to(4,4)\)
\((-3,-2)\to(2,3)\)
\((-8,-4)\to(4,8)\)