Question

The graph shows a reflection in the x-axis. The matrix M such that, for any point (x, y), M(x, y) = (x', y') is

Note: Both attachments below are regarded to this question

Answer 1

This is a reflection about the x-axis.

Explanation:

A reflection about the x-axis has the rule

[x,y]-> [x,-y].

Therefore

M[x,y] = [x,-y}

Let M=

|a b|

|c d|

Then the matrix multiplication gives

ax+by=x.............(1)

cx+dy=-y............(2)

Solving the previous equations (1) and (2) gives

a=1, b=0

c=0, d=-1

giving M as

|1 0|

|0 -1|