Question

( 3,4) write the new coordinates after the following transformations. reflection over the x axis. reflection over the y axis. reflection over the line y=x

Answer 1

Let A be the point (3,4). Then, the first transformation is a reflection over te x-axis, which can be found using the following expression:

$r_x(x,y)=(x,-y)$

in this case, we have:

$r_x(A)=r_x(3,4)=(3,-4)=A_1$

the next transformation is a reflection over the y-axis, which has the following general rule:

$r_y(x,y)=(-x,y)$

then, applying this transformation,we get:

$r_y(A_1)=r_y(3,-4)=(-3,-4)=A_2$

finally, the reflection over the line y = x has the following function:

$r_{y=x}(x,y)=(-x,-y)$

then, we have:

$r_{y=x}(A_2)=r_{y=x}(-3,-4)=(-4,-3)$

therefore, the new coordinates after the transformations are (-4,-3)