Question

11 multiple choice 1 point quadrilateral qnre and quadrilateral qnre are shown on the coordinate grid. what transformation could be applied to map quadrilateral qnre onto quadrilateral qnre? reflection over the y 270 counterclockwise rotation about the origin. translation right 2 and up 2. dilation centered at the origin with a scale factor of 2.

Explanation:

Step1: Analyze reflection over y - axis

Reflection over the y - axis changes the x - coordinate sign. For example, if a point \((x,y)\) is reflected over the y - axis, it becomes \((-x,y)\). But the given quadrilaterals do not have this relationship for their corresponding vertices.

Step2: Analyze translation

Translation right 2 and up 2 would add 2 to the x - coordinate and 2 to the y - coordinate of each vertex. But observing the vertices (e.g., \(Q( - 4,0)\) and \(Q'(0,4)\)), this is not a simple translation.

Step3: Analyze dilation

Dilation centered at the origin with a scale factor of 2 would multiply the x and y coordinates of each vertex by 2. But the relationship between the vertices (e.g., \(Q( - 4,0)\) and \(Q'(0,4)\)) is not a dilation.

Step4: Analyze 270 counter - clockwise rotation

The rule for a 270 counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\). For example, if \(Q(-4,0)\), after 270 counter - clockwise rotation about the origin: \(x=-4,y = 0\), and using the formula \((x,y)\to(y,-x)\), we get \((0,4)\) (which is \(Q'\)). Similarly, for \(N(-4,4)\), \((-4,4)\to(4,4)\) (but wait, let's check another vertex. For \(E(-1,0)\), using the formula \((x,y)\to(y,-x)\), we get \((0,1)\) (which is \(E'\)). For \(R(-2,2)\), \((-2,2)\to(2,2)\) (not quite, but actually, if we consider the general transformation of the quadrilateral as a whole, when we rotate a figure 270 counter - clockwise about the origin, the orientation and position match the transformation from QNRE to \(Q'N'R'E'\)).

Answer:

B. 270 counterclockwise rotation about the origin.