WRITE A RULE TO DESCRIBE EACH REFLECTION WORKSHEET

Write a rule to describe each transformation.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

L(0, 1), K(0, 2), J(3, 3), I(5, 1)

to

L'(0, -1), K'(0, -2), J'(3, -3), I'(5, -1)

Solution

Problem 7 :

Find the coordinates of the figure after reflecting in the x-axis.

a) A (3, 2), B (4, 4), C (1, 3)

b) M(−2, 1), N(0, 3), P(2, 2)

c) H(2, −2), J(4, −1), K(6, −3), L(5, −4)

d) D(−2, −1), E(0, −2), F(1, −5), G(−1, −4)

Solution

Problem 8 :

Reflect the triangle in the line y = x. How are the x and y-coordinate of the image related to the x and y-coordinate of the original triangle ?

Solution

Problem 1 :

L (0, 1), K (0, 2), J (3, 3), I (5, 1)

to

L' (0, -1), K' (0, -2), J' (3, -3), I' (5, -1)

Solution

Problem 2 :

H (-3, -5), I (-5, -2), J (-1, -1), K (0, -4)

to

H' (-3, 5), I' (-5, 2), J' (-1, 1), K' (0, 4)

Solution

Problem 3 :

P (-4, -3), Q (-1, 1), R (0, -4)

to

P'(-4, 3), Q'(-1, -1), R'(0, 4)

Solution

Problem 4 :

E (3, 1), F (3, 4), G (5, 1)

to

E' (-1, -3), F' (-4, -3), G' (-1, -5)

Solution

Problem 5 :

The reflection of a point P in the y-axis is P' (– 4, –2). The coordinates of point P are:

(a) (– 4, 2)     (b) (4, 2)      (c) (4, –2)      (d) (–2, 4) 

Solution

Problem 6 :

Point (0, –2) is invariant under reflection in:

(a) x-axis      (b) y-axis     (c) origin     (d) none

Solution

Problem 7 :

Point (5, 0) is invariant under reflection in :

(a) x-axis     (b) y-axis     (c) origin     (d) none

Solution

Problem 8 :

The points (3, 0) and (–1, 0) are invariant points under reflection in the line L1, while the points (0, –3) and (0, 1) are invariant points under reflection in the line L2

(a) Name the lines L1 and L2

(b) Write down the images of the points P(3, 4) and Q(–5, –2) on reflection in L1. Name the images as P′ and Q′ respectively.

(c) Write down the images of P and Q on reflection in L2. Name the images as P′′ and Q′′ respectively.

(d) State or describe a single transformation that maps P′ onto P′′.

Solution

Graph the image of the figure using the transformation given.

Problem 1 :

Solution

Problem 2 :

Reflection across the y-axis

Y (2, 2)

Solution

Problem 3 :

Reflection on y-axis

Solution

Problem 4 :

Solution

Problem 5 :

Reflection across y-axis

Solution

Problem 6 :

Reflection across the y-axis

D (-2, -3), E (2, -2) and F (3, -4)

Solution

Problem 7:

Solution

Problem 8:

Reflection across the y-axis

J (-2, -4), K (-3, -1), L (-1, -1), M (2, -5)

Solution

Problem 9 :

The vertices of a rectangle are A(−4, −3), B(−4, −1), C(−1, −1), and D(−1, −3).

a. Draw the rectangle and its reflection in the x-axis.

b. Draw the rectangle and its reflection in the y-axis.

c. Are the images in parts (a) and (b) the same size and shape? Explain.

Solution

Problem 10 :

The vertices of a quadrilateral are P(−2, 5), Q(−1, −1), R(−4, 2), and S(−4, 4). Draw this quadrilateral and its reflection in the y-axis. What are the coordinates of the image?

Solution

Problem 11 :

Given the point (3, 4), find its reflection over the x-axis.

Solution

Problem 12 :

Given the point (3, 4), find its reflection over the y-axis

Solution

Problem 13 :

For the function f(x) = 2x - 3, graph both f(x) and its reflection over the x-axis on the same set of axes.

Solution

Problem 14 :

Point P is first reflected in x-axis to P′. P′ is then reflected in y-axis to P′′(–2, 5). The coordinates of P are:

(a) (2, 5)      (b) (–2, –5)      (c) (2, –5)      (d) (–5, 2)

Solution

Problem 15 :

The vertices of a triangle are A (−1, 1), B (2, 3), and C (6, 3). Draw this triangle and its reflection in the x-axis. What are the coordinates of the image?

Solution