Question

Quadrilateral WXYZ will be rotated 180° about the origin and then reflected across the Y axis. Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.​

Answer 1

Answer:

The quadrilaterals will be congruent  

The quadrilateral will now appear in Quadrant 2

Step-by-step explanation:

Given

$W = (-7,-2)$

$X= (-4,-2)$

$Z = (-6,-6)$

$Y =(-3,-7)$

Rotation across 180 degrees

Reflection across y-axis

Required

The true statement

Using point W as a point of reference; We have:

$W = (-7,-2)$

1. Rotation across 180 degrees

The rule is:

$(x,y) \to (-x,-y)$

So:

$W(-7,-2) \to W'(7,2)$

2. Reflection across y-axis

The rule is:

$(x,y) \to (-x,y)$

So:

$W'(7,2) \to (-7,2)$

Using the above transformation on the other points; We have:

$W(-7,-2) \to W"(-7,2)$

$X (-4,-2) \to X "(-4,2)$

$Z (-6,-6) \to Z" (-6,6)$

$Y(-3,-7) \to Y"(-3,7)$

Plot the above points on a grid (see attachment).

From the grid, we can conclude that: the quadrilaterals will be congruent  , and it will appear in Quadrant 2.