Question

the graph shows triangles qrs and qrs. which of the following transformations maps qrs onto qrs? translation down 6 units translation down 20 units reflection across the x - axis reflection across the y - axis rotation 90° clockwise around the origin rotation 90° counterclockwise around the origin rotation 180° around the origin

Explanation:

Step1: Analyze translation

Translation down 6 units or 20 units would just move the triangle vertically without changing its orientation or mirror - image. By observing the graph, we can see that the orientation has changed, so these are not correct.

Step2: Analyze reflection across axes

If we reflect across the x - axis, the (x,y) coordinates of the points change to (x, - y). If we reflect across the y - axis, the (x,y) coordinates change to (-x,y). By observing the graph, the orientation of the triangle is not consistent with either of these reflections.

Step3: Analyze rotations

For a 90° clockwise rotation around the origin, the transformation rule for a point (x,y) is (y, - x). For a 90° counter - clockwise rotation around the origin, the rule is (-y,x). For a 180° rotation around the origin, the rule for a point (x,y) is (-x, - y). By observing the orientation and position of the vertices of triangle QRS and Q'R'S', we can see that a 180° rotation around the origin maps QRS onto Q'R'S'.

Answer:

rotation 180° around the origin