Point b (6,9) is reflected across the line y=x and then dilated by a factor of 1/3 using the origin as the center of dilation. what is the resultant point

(3, 2)  

Step-by-step explanation:

(a) Reflection

When you reflect a point across the line y = x, the x- and y-coordinates are interchanged.

Thus, if the coordinates of the original point are (6, 9), those of the reflected point are (9, 6).

(b) Dilation

When you dilate a point by a factor of ⅓ from the origin, you multiply its coordinates by the same factor.

Thus, if the coordinates of the original point are (9,6), those of the dilated point are (3, 2).

The graph below shows the point at (6,9) being reflected about the

line y = x  to (9, 6) and then being dilated along a ray from the origin

to (3, 2).