Question

1. The diagram given below shows the unit square OABC.



The unit square OABC is transformed by matrix N $\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right]$


a) Find the coordinates of O’A’B’ C’, the images of O, A, B and C under the transformation by matrix N.
b) Describe fully the transformation given by matrix N.

Answer 1

Answer:

A matrix is a rectangular arrangement of numbers into rows and columns. Each number in a matrix is referred to as a matrix element or entry. For example, matrix ...

Step-by-step explanation:

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Answer 2

Answer:

a) since unit square we get the coordinates (x,y);

O=(0,0)

A=(1,0)

B=(1,1)

C=(0,1)

using matrix $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] . \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}x'\\y'\end{array}\right]$

we find O'=$\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right] . \left[\begin{array}{ccc}0\\0\end{array}\right] = \left[\begin{array}{ccc}x'\\y'\end{array}\right]$

             O'= $\left[\begin{array}{ccc}1*0 + 0*0\\ 0*0 + -1*0\end{array}\right] = \left[\begin{array}{ccc}x'\\y'\end{array}\right]$

               (x',y')= (0,0)

do the same for A,B,C and we get the coordinates for A',B'C'

thus O'=(0,0)

       A'=(1,0)

       B'=(1,-1)

       D'=(0,-1)

draw the graph using the coordinates

Step-by-step explanation:

b) the transformation is on mirror line x=0