Question

(x,y)→(x,y - 8)
d( , ) d( , )
e( , ) e( , )
f( , ) f( , )

Explanation:

Step1: Determine original coordinates

By observing the graph, assume each grid - square represents 1 unit. Point D is 1 unit to the right of the y - axis and 3 units above the x - axis, so D(1,3). Point E is 3 units to the right of the y - axis and 3 units above the x - axis, so E(3,3). Point F is at the origin, so F(0,0).

Step2: Apply the transformation rule

The transformation rule is (x,y)→(x,y - 8).
For point D(1,3): Substitute x = 1 and y = 3 into the rule. The new y - coordinate is 3−8=-5, so D'(1, - 5).
For point E(3,3): Substitute x = 3 and y = 3 into the rule. The new y - coordinate is 3−8=-5, so E'(3, - 5).
For point F(0,0): Substitute x = 0 and y = 0 into the rule. The new y - coordinate is 0−8=-8, so F'(0, - 8).

Answer:

D(1,3), D'(1, - 5)
E(3,3), E'(3, - 5)
F(0,0), F'(0, - 8)