What set of reflections would carry trapezoid abcd onto itself? y=x, x-axis, y=x, y-axis x-axis, y=x, x-axis, y=x y-axis, x-axis, y-axis x-axis, y-axis, y-axis

y=x, x-axis, y=x, y-axis

Step-by-step explanation:

The correct answer is:

y=x, x-axis, y=x, y-axis

When a reflection takes place across the line y=x, then it maps every point (x, y) to (y, x).

This means that the mapping switches the coordinates, but does not negate them.

This means for A(1, -1), we will have A'(-1, 1); B(2, -2)→B'(-2, 2); C(3, -2)→C'(-2, 3); and D(4, -1)→D'(-1, 4).

And we get new points as :

A'(-1, 1)→A''(-1, -1); B'(-2, 2)→B''(-2, -2); C'(-2, 3)→C''(-2, -3); and D'(-1, 4)→D''(-1, -4).

Now again reflecting across the line y=x will again switch the x- and y-coordinates to :

A''(-1, -1)→A'''(-1, -1); B''(-2, -2)→B'''(-2, -2); C''(-2, -3)→C'''(-3, -2); and D''(-1, -4)→D'''(-4, -1).

And we know that while reflecting across the y-axis, the transformation will negate the x-coordinate:

So, new coordinates are :

A'''(-1, -1)→(1, -1); B'''(-2, -2)→(2, -2); C'''(-3, -2)→(3, -2); and D'''(-4, -1)→(4, -1).

Finally, we can see that these points are the same as our original points.

So, option A is the answer.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have