Question

The transformation represented by the matrix

[
1
0
0
−
1
]
[
1
0
​

0
−1
​
] is a reflection across which axis?

a) X-axis

b) Y-axis

c) Origin

d) Diagonal axis

Answer 1

The matrix [ 1 0 0 -1 ] represents a reflection across the X-axis, as it negates only the y-coordinate of points in the coordinate system.

Step-by-step explanation:

The transformation represented by the matrix [ 1 0 0 -1 ] is a reflection across an axis in the coordinate system. When a point (x, y) is multiplied by this matrix, the result is (x, -y), which means the x-coordinate stays the same while the y-coordinate is negated. This means that all the points are reflected over the x-axis, as the reflection flips the points over the axis that remains unchanged. Therefore, the correct answer is a) X-axis.