Question

a triangle has vertices at (-3, 4), (-1, 0), and (-4, 0). what are the coordinates of the vertices after it is rotated 180° about the origin? enter the correct coordinates in the boxes. show hints (-1, 3), (0, 1), (0, 4) × keypad with numbers 7,8,9,+,4,5,6,-,1,2,3,×,0,.,,,÷,×,=

Explanation:

Step1: Recall 180° rotation rule

To rotate a point \((x, y)\) 180° about the origin, the rule is \((x, y) \to (-x, -y)\).

Step2: Apply rule to first vertex \((-3, 4)\)

For \((-3, 4)\), \(x = -3\), \(y = 4\). So \(-x = -(-3)=3\), \(-y = -4\). The new point is \((3, -4)\).

Step3: Apply rule to second vertex \((-1, 0)\)

For \((-1, 0)\), \(x = -1\), \(y = 0\). So \(-x = -(-1)=1\), \(-y = -0 = 0\). The new point is \((1, 0)\).

Step4: Apply rule to third vertex \((-4, 0)\)

For \((-4, 0)\), \(x = -4\), \(y = 0\). So \(-x = -(-4)=4\), \(-y = -0 = 0\). The new point is \((4, 0)\).

Answer:

\((3, -4)\), \((1, 0)\), \((4, 0)\)