Answer:
A'''(-1,3), B'''(2,2) and C'''(3,-3)
Step-by-step explanation:
Hello There!
So the first thing we need to do is reflect the coordinates given over the y = x line which would be a straight line across the origin with a rate of change of 1
The rule for a reflection over the y = x line is (x,y) ----> (y,x)
so pretty much we're just flipping the y and x values
(1,6) ---> (6,1)
(2,9) ---> (9,2)
(7,10) ---> (10,7)
so the new coordinates of A'B'C' are A'(6,1) , B'(9,2), and C'(10,7)
Now we want to reflect the points over the x axis
The rule for reflection over the x axis is (x,y) ----> (x,-y)
so the x value stays the same and the y values sign just get flipped so if the y value was originally negative then it will change to positive vise versa
(6,1) ---> (6,-1)
(9,2) ---> (9,-2)
(10,7) ---> (10,-7)
So the coordinates of A''B''C'' are A''(6,-1) , B''(9,-2), and C''(10,-7)
Our final step is to translate 7 units to the left 4 units up
so the rule would be (x,y) ----> (x - 7, y + 4)
6-7=-1 | -1+4=3
(6,-1) ---> (-1,3)
9-7=2 | -2+4=2
(9,-2) ---> (2,2)
10-7=3 | -7+4=-3
(10,-7) ---> (3,-3)
so the after the three transformations the coordinates would be
A'''(-1,3), B'''(2,2) and C'''(3,-3)
