   Chapter 10.1, Problem 12E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Points A and B have symmetry with respect to point C ( 2 ,   3 ) .Find the coordinates of B if A is the point: a) ( 3 ,   - 4 ) c) ( 5 ,   0 ) b) ( 0 ,   2 ) d )   ( a , b )

To determine

(a)

To find:

The coordinates of B if A is the given point (3, -4) and the points are symmetry with respect to point C (2, 3).

Explanation

The coordinates of A is (3, -4).

The coordinates of B is (x2, y2).

And the points are symmetry with respect to the point (2, 3).

Hence, (2, 3) is the midpoint of the points A and B.

Determining coordinates of B using midpoint formula,

xm,ym=x1+x22,y1+y22

xm,ym are the midpoints.

x1, y1=(3, -4)

xm,ym=(2, 3)

To determine

(b)

To find:

The coordinates of B if A is the given point (0, 2) and the points are symmetry with respect to point C (2, 3).

To determine

(c)

To find:

The coordinates of B if A is the given point (5, 0) and the points are symmetry with respect to point C (2, 3).

To determine

(d)

To find:

The coordinates of B if A is the given point (a, b) and the points are symmetry with respect to point C (2, 3).

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