HOW TO FIND REFLECTION OF MATRIX ABOUT X-AXIS AND Y-AXIS

A reflection occurs when every point on a preimage is reflected across a  line of symmetry using a reflection matrix. 

Problem 1 :

The triangle PQR has coordinates

P(3, 5), Q(6, 5) and R(6, 7)

Determine the coordinates of the image of triangle PQR under a reflection in the x- axis.

Solution :

Reflection in the x- axis :

P(3, 5) ==> P'(3, -5)

Q(6, 5) ==> Q'(6, -5)

R(6, 7) ==> R'(6, -7)

Problem 2 :

Find the coordinates of the vertices of the image of pentagon ORSTU with

Q(1, 3) R(3, 2) S(3, -1) T(1, -2) and U(-1, 1)

after a reflection across y-axis.

Solution :

Problem 3 :

Graph the figure and its image after the given transformation.

a reflection in the y-axis.

Solution :

Problem 4 :

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

Reflection across y = x

Solution :

Problem 5 :

The coordinates of the vertices of a polygon are given. Represent each transformation with matrices. Then express the coordinates of the vertices of the image as a matrix.

Q(2, 0), R(0, -2), S(-2, 0); a reflection in y = -x

Solution :

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

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

S(-2, 0) ==> S(0, 2)

Problem 6 :

Use the rectangle below

i) Write the coordinates in vertex form

ii)  Find the coordinate of the image after a reflection over the x-axis.

Solution :

A(0, 4) B(5, 4) C(5, 0) and D(0, 0).

Reflection over x-axis.