Question

test prep a pentagon has vertices at $(-1, -1)$, $(-5, -2)$, $(-6, -4)$, $(-4, -7)$, and $(-2, -3)$. if the pentagon is rotated $180^circ$ clockwise, what are the coordinates of the vertices of the image?
enter the correct answers in the boxes.
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$(\square, \square)$, $(\square, \square)$, $(\square, \square)$, $(\square, \square)$, $(\square, \square)$

Explanation:

Step1: Recall 180° rotation rule

To rotate a point \((x, y)\) 180° clockwise (or counterclockwise), the rule is \((x, y) \to (-x, -y)\).

Step2: Apply rule to each vertex

• For \((-1, -1)\):
• New \(x\): \(-(-1) = 1\)
• New \(y\): \(-(-1) = 1\)
• So, \((1, 1)\)
• For \((-5, -2)\):
• New \(x\): \(-(-5) = 5\)
• New \(y\): \(-(-2) = 2\)
• So, \((5, 2)\)
• For \((-6, -4)\):
• New \(x\): \(-(-6) = 6\)
• New \(y\): \(-(-4) = 4\)
• So, \((6, 4)\)
• For \((-4, -7)\):
• New \(x\): \(-(-4) = 4\)
• New \(y\): \(-(-7) = 7\)
• So, \((4, 7)\)
• For \((-2, -3)\):
• New \(x\): \(-(-2) = 2\)
• New \(y\): \(-(-3) = 3\)
• So, \((2, 3)\)

Answer:

\((1, 1)\), \((5, 2)\), \((6, 4)\), \((4, 7)\), \((2, 3)\)