Question

Calculate this reflection of the triangle:

Answer 1

Answer:

a = 3, b = 0, c = 0, d = -2

Step-by-step explanation:

To find the reflection Multiply the matrices

∵ The dimension of the first matrix is 2 × 2

∵ The dimension of the second matrix is 2 × 3

1. Multiply the first row of the 1st matrix by each column in the second matrix add the products of each column to get the first row in the 3rd matrix.

2. Multiply the second row of the 1st matrix by each column in the second matrix add the products of each column to get the second row of the 3rd matrix

$\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right]$  × $\left[\begin{array}{ccc}0&3&0\\0&0&2\end{array}\right]$  = $\left[\begin{array}{ccc}(1*0+0*0)&(1*3+0*0)&(1*0+0*2)\\(0*0+-1*0)&(0*3+-1*0)&(0*0+-1*2)\end{array}\right]=\left[\begin{array}{ccc}0&3&0\\0&0&-2\end{array}\right]$

Compare the elements in the answer with the third matrix to find the values of a, b, c, and d

∴ a = 3

∴ b = 0

∴ c = 0

∴ d = -2