Question

2) The coordinates of the vertices of quadrilateral ABCD are A(-1,8),

B(0,4), C(-2,1), and D(-4,3). Quadrilateral A'B'C'D' is the image of
quadrilateral ABCD after a rotation of 180° about the origin. State the
coordinates of the vertices of A'B'C'D'.

Answer 1

The coordinates of vertices of A'B'C'D' are:

A'(1,-8), B'(0,-4), C'(2,-1) and D'(4,-3)

Explanation:

When a point (h,k) is roated 180 degrees about the origin it becomes (-h,-k) which means that the new point after rotation is the negative of the previous.

Given vertices are:

A(-1,8), B(0,4), C(-2,1), and D(-4,3)

The new vertices will be:

`A(-1,8) => A'(1,-8)\\B(0,4)=> B'(0,-4)\\C(-2,1)=> C'(2,-1)\\D(-4,3)=> D'(4,-3)`

The coordinates of vertices of A'B'C'D' are:

A'(1,-8), B'(0,-4), C'(2,-1) and D'(4,-3)