Question

If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie? Rectangle formed by ordered pairs A at negative 4, 1, B at negative 4, 2, C at negative 1, 2, D at negative 1, 1. a (1, −1) b (1, 1) c (−4, −1) d (−4, 1)

Answer 1

The answer is d (-4,1)

Answer 2

Answer: d. (−4, 1)

Explanation:

The rule of reflection across y axis is given by :-

`(x,y)\rightarrow\ (-x,y)`

The rule of reflection across x axis is given by :-

`(x,y)\rightarrow\ (x,-y)`

The rule of rotation of 180° is given by :-

`(x,y)\rightarrow\ (-x,-y)`

Given point A : (-4,1)

After reflection across y-axis the image of A becomes :-

`(-4,1)\rightarrow\ (4,1)`

After reflection across x-axis the image of point (4,1) becomes :-

`(4,1)\rightarrow\ (4,-1)`

After rotation of 180° the image of point (4,-1) becomes :-

`(4,-1)\rightarrow\ (-4,1)`

Hence, the point A' lies at (-4,1) .