Question

for #s 9 and 10, find the coordinates of the given vertices and the rule used.

1. r(-7, -5), s(-1, -2), t(-1, -5) 90° clockwise about the origin
2. j(-4, 4), k(-3, 4), l(-1, 1), m(-4, 1) 180° about the origin

Explanation:

Step1: Recall the rotation rules

The rule for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, -x)\). The rule for a \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x,-y)\).

Step2: Apply the \(90^{\circ}\) clockwise rotation rule to points \(R(-7,-5)\), \(S(-1,-2)\), \(T(-1,-5)\)

For point \(R(-7,-5)\):
Substitute \(x = - 7\) and \(y=-5\) into \((x,y)\to(y, -x)\).
We get \((-5,7)\).
For point \(S(-1,-2)\):
Substitute \(x=-1\) and \(y = - 2\) into \((x,y)\to(y, -x)\).
We get \((-2,1)\).
For point \(T(-1,-5)\):
Substitute \(x=-1\) and \(y=-5\) into \((x,y)\to(y, -x)\).
We get \((-5,1)\).

Step3: Apply the \(180^{\circ}\) rotation rule to points \(J(-4,4)\), \(K(-3,4)\), \(L(-1,1)\), \(M(-4,1)\)

For point \(J(-4,4)\):
Substitute \(x=-4\) and \(y = 4\) into \((x,y)\to(-x,-y)\).
We get \((4,-4)\).
For point \(K(-3,4)\):
Substitute \(x=-3\) and \(y = 4\) into \((x,y)\to(-x,-y)\).
We get \((3,-4)\).
For point \(L(-1,1)\):
Substitute \(x=-1\) and \(y = 1\) into \((x,y)\to(-x,-y)\).
We get \((1,-1)\).
For point \(M(-4,1)\):
Substitute \(x=-4\) and \(y = 1\) into \((x,y)\to(-x,-y)\).
We get \((4,-1)\).

Answer:

For the \(90^{\circ}\) clockwise rotation:

• \(R(-7,-5)\) rotates to \((-5,7)\)
• \(S(-1,-2)\) rotates to \((-2,1)\)
• \(T(-1,-5)\) rotates to \((-5,1)\)

The rule is \((x,y)\to(y, -x)\)

For the \(180^{\circ}\) rotation:

• \(J(-4,4)\) rotates to \((4,-4)\)
• \(K(-3,4)\) rotates to \((3,-4)\)
• \(L(-1,1)\) rotates to \((1,-1)\)
• \(M(-4,1)\) rotates to \((4,-1)\)

The rule is \((x,y)\to(-x,-y)\)