Question

What set of reflections would carry trapezoid ABCD onto itself?

a. y=x, x-axis, y=x, y-axis/p>
b. x-axis, y=x, x-axis, y=x
c. y-axis, x-axis, y-axis
d. x-axis, y-axis, y-xis

Answer 1

a. y=x, x-axis, y=x, y-axis

Explanation:

We have,

'Reflection across x-axis changes (x,y) to (x,-y)'

'Reflection across y-axis changes (x,y) to (-x,y)'

'Reflection across y=x changes (x,y) to (y,x)'

As, ABCD have co-ordinates A(1,-1), B(4,-1), C(2,-2) and D(3,-2).

We see that, on applying the reflections in the sequence 'y=x, x-axis, y=x, y-axis', the following table is obtained,

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

A=(1,-1) (-1,1) (-1,-1) (-1,-1) (1,-1)

B=(4,-1) (-1,4) (-1,-4) (-4,-1) (4,-1)

C=(2,-2) (-2,2) (-2,-2) (-2,-2) (2,-2)

D=(3,-2) (-2,3) (-2,-3) (-3,-2) (3,-2)

Hence, the sequence 'y=x, x-axis, y=x, y-axis' maps ABCD onto itself.