Which figure is the image produced by applying the composition t 0,3 o r0,90 to figure r? a. figure h b. figure i c. figure j d. figure r

We are given original image R.

It is being translated by (0,3) first and then rotated by a positive angle 90 degrees.

Translation by (0,3) represents (x,y) --> (x, y+3) rule.

Positive 90 degree rotation represents, counterclockwise rotation.

The rule for counterclockwise rotation is (x,y) --> (-y,x).

Therefore, final rule for would be

(x,y) --> ( -y,x+3 )

Let us take a coordinate of R on y-axis as (0,-4).

Now if we apply rule (x,y) --> ( -y,x+3 ) we get

(0,-4)  --> (-(-4), 0+3) = (4,3).

Let us check the figure with coordinate (4,3).

We can clearly see that Figure H has transformed coordinate (4,3).