Question

the graph shows triangles opq and opq. which sequence of transformations maps opq onto opq? a reflection across the line y = x followed by a translation left 2 units a reflection across the line x = 1 followed by a translation up 11 units a reflection across the line y = 1 followed by a translation left 10 units

Explanation:

Step1: Analyze reflection across y = x

Reflection across y = x swaps the x - and y - coordinates of points. But the orientation and position of the triangles do not match the result of a y = x reflection followed by a left - 2 translation.

Step2: Analyze reflection across x = 1

The distance of points of OPQ from x = 1 and their corresponding points in O'P'Q' do not match the pattern of a reflection across x = 1 followed by an up - 11 translation.

Step3: Analyze reflection across y = 1

Let's assume a point (x,y) in OPQ. The distance from y = 1 is d=y - 1. After reflection across y = 1, the new y - coordinate is y'=1-(y - 1)=2 - y.

Step4: Analyze left - 10 translation

After reflection across y = 1, if we translate the reflected points left 10 units (subtract 10 from the x - coordinate), we can match the points of OPQ to O'P'Q'. For example, if we take a vertex of OPQ and first reflect it across y = 1 and then translate it left 10 units, we get the corresponding vertex of O'P'Q'.

Answer:

a reflection across the line y = 1 followed by a translation left 10 units