Question

remy draws figure efgh on a coordinate plane, as shown. remy rotates figure efgh 180° counterclockwise around the origin to form figure efgh and then translates the image 6 units down to form figure efgh. what are the coordinates of vertex f? use the number pad to enter your answers in the boxes. ( )

Explanation:

Step1: Apply rotation rule

For a \(180^{\circ}\) counter - clockwise rotation around the origin, if \(F=(2,-4)\), then \(F'=(-2,4)\) using the rule \((x,y)\to(-x,-y)\).

Step2: Apply translation rule

For a translation 6 units down, the \(x\) - coordinate of \(F'\) stays the same (\(x=-2\)), and the \(y\) - coordinate of \(F'\) is \(y = 4-6=-2\). So \(F''=(-2,-2)\).

Answer:

<Let's assume the coordinates of point \(F\) are \((x,y)\). After a \(180^{\circ}\) counter - clockwise rotation around the origin, the rule for a \(180^{\circ}\) rotation of a point \((x,y)\) is \((x,y)\to(-x,-y)\). Let the coordinates of \(F\) be \((2, - 4)\) (assuming from the general position in the figure). After rotation, \(F'\) has coordinates \((-2,4)\). After translating \(F'\) 6 units down, the \(x\) - coordinate remains the same and the \(y\) - coordinate is decreased by 6. So the coordinates of \(F''\) are \((-2,-2)\)>