Question

Which of the following compositions will map figure Z onto figure R and then onto figure J? A. clockwise rotation and translation B. glide reflection C. reflection and rotation D. double reflection

I think its C but I don't know

Answer 1

Answer: The correct option is (D) double reflection.

Step-by-step explanation: We are given to select the correct composition that will map figure Z onto figure R and then onto figure J.

From the figure, we note that

the co-ordinates of the vertices of the figure Z are (0, 2), (1, 2), (4, 5) and (1, 4).

The co-ordinates of the vertices of the figure R are (0, 2), (-1, 2), (-4, 5) and (-1, 4).

The co-ordinates of the vertices of the figure J are (0, -2), (-1, -2), (-4, -5) and (-1, -4).

We know that, if a point is getting reflected over Y-axis, then its co-ordinates will change according to the rule (x, y) ⇒ (-x, y).

So, if the figure Z is reflected over Y-axis, then its co-ordinates will become

(0, 2) ⇒ (0, 2),

(1, 2) ⇒ (-1, 2),

(4, 5) ⇒ (-4, 5)

and

(1, 4) ⇒ (-1, 4).

These are the co-ordinates of the vertices of figure R, so first transformation is a reflection.

Again, if we reflect the figure R over X-axis, then the co-ordinates of the vertices will change according to the rule (x, y) ⇒ (x, -y).

So, the vertices of figure R will become

(0, 2) ⇒ (0, -2),

(-1, 2) ⇒ (-1, -2),

(-4, 5) ⇒ (-4, -5)

and

(-1, 4) ⇒ (-1, -4).

Thus, the required compositions that will map figure Z onto figure R and then onto figure J are reflection and reflection, .i.e., double reflection.

Option (D) is the correct option.

Answer 2

D

Explanation:

Reflect Z across y-axis. This maps point Z (1,2) onto (-1.2). Then reflect across the x-axis by moving point (-1,2) to (-1,-2).