REFLECTION ACROSS Y EQUALS NEGATIVE X

Graph the image of the figure using the transformation given.

Problem 1 :

Reflection across the line y = -x.

Solution :

By observing the coordinates of the vertices of the triangle given above.

L (1, 2), G (3, 4) and Q (4, -1)

Rule for reflection across y = -x :

(x, y) ==> (-y, -x)

Find the coordinates of the vertices of each figure after the given transformation.

Problem 2 :

Reflection across the y = -x

T(2, 2), C(2, 5), Z(5, 4), F(5, 0)

Solution :

T(2, 2), C(2, 5), Z(5, 4), F(5, 0)

Rule for reflection across y = -x :

(x, y) ==> (-y, -x)

T (2, 2)  ==> T' (-2, -2)

C (2, 5) ==> C' (-5, -2)

Z (5, 4) ==> Z' (-4, -5)

F (5, 0) ==> F (0, -5)

Find the coordinates of the vertices of each figure after the given transformation.

Problem 3 :

Reflection across the line y = -x.

Solution :

By observing the figure, the coordinates are 

W (-4, 2), B (-3, -1), Y (-1, 1), Z (-2, 3)

Rule for reflection across y = -x :

(x, y) ==> (-y, -x)

W (-4, 2)  ==> W' (-2, 4)

B (-3, -1) ==> B' (1, 3)

Y (-1, 1) ==> Y' (-1, 1)

Z (-2, 3) ==> Z' (-3, 2)

Graph the image of the figure using the transformation given.

Problem 4 :

Reflection across the line y = -x.

Solution :

By observing the figure, the coordinates are 

R (-3, 3), C (0, 0), V (-1, 5)

Rule for reflection across y = -x :

(x, y) ==> (-y, -x)

R (-3, 3)  ==> R' (-3, 3)

C (0, 0) ==> C' (0, 0)

V (-1, 5) ==> V' (-5, 1)

Problem 5 :

Reflection across the line y = -x.

Solution :

By observing the figure, the coordinates are 

J (-1, -3), R (-3, 2), Z (0, 2) and Y (2, -2)

Rule for reflection across y = -x :

(x, y) ==> (-y, -x)

J (-1, -3)  ==> J' (3, 1)

R (-3, 2) ==> R' (2, 3)

Z (0, 2) ==> Z' (-2, 0)

Y (2, -2)  ==> Y' (2, -2)

Problem 6 :

graph the polygon and its image after a reflection in the given line.

y = x

Solution :

The points shown are A(6, -3), B(1, -2) and C(4, 1)

Rule for reflection about y = x is (x, y) ==> (y, x)

A (6, -3) ==> A' (-3, 6)

B (1, -2) ==> B' (-2, 1)

C (4, 1) ==> C' (1, 4)

Problem 7 :

graph the polygon and its image after a reflection in the given line.

y = x

Solution :

The points shown are A (2, -1), B (-1, 2) C (2, 3) and D (4, 2)

Rule for reflection about y = x is (x, y) ==> (y, x)

A (2, -1) ==> A' (-1, 2)

B (-1, 2) ==> B' (2, -1)

C (2, 3) ==> C' (3, 2)

D (4, 2) ==> D' (2, 4)

Problem 8 :

graph the polygon and its image after a reflection in the given line.

y = -x

Solution :

The points shown are A (-3, 2), B (1, -1) C (-2, -2) and D (-4, -1)

Rule for reflection about y = -x is (x, y) ==> (-y, -x)

A (-3, 2) ==> A' (-2, 3)

B (1, -1) ==> B' (1, -1)

C (-2, -2) ==> C' (2, 2)

D (-4, -1) ==> D' (1, 4)

Problem 9 :

graph the polygon and its image after a reflection in the given line.

y = -x

Solution :

The points shown are A (1, 2), B (4, 2) and C (3, -2)

Rule for reflection about y = -x is (x, y) ==> (-y, -x)

A (1, 2) ==> A' (-2, -1)

B (4, 2) ==> B' (-2, -4)

C (3, -2) ==> C' (2, -3)

Problem 10 :

Graph triangle JKL with vertices J(3, 1) K (4, 2) and L(1, 3) and its image after the glide reflection.

Translation (x, y) ==> (x - 6, y - 1)

Reflection : in the line y = -x

Solution :

Given points are J(3, 1) K (4, 2) and L(1, 3)

Reflection across y = -x :

J (3, 1) ==> J' (-1, -3)

K (4, 2) ==> K' (-2, -4)

L (1, 3) ==> L' (-3, -1)

Translation of 6 units left and 1 unit down :

J' (-1, -3) ==> J'(-1 - 6, -3 - 1) ==> J'(-7, -4)

K' (-2, -4) ==> K' (-2 - 6, -4 - 1) ==> K' (-8, -5)

L' (-3, -1) ==> L' (-3 - 6, -1 - 1) ==> L' (-9, -2)