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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Points A and B have symmetry with respect to point C. Find the coordinates of C given the point:

a) A ( 3 ,   - 4 ) and B ( 5 ,   - 1 ) c) A ( 5 ,   - 3 ) and B ( 2 ,   1 )
b) A ( 0 ,   2 ) and B ( 0 ,   6 ) d) A ( 2 a ,   0 )   a n d   B ( 0 ,   2 b )

To determine

(a)

To find:

The coordinates of C given the points A (3, -4) and B (5, -1) and the points A and B are symmetry with respect to point C.

Explanation

The coordinates of A is (3, -4).

The coordinates of B is (5, -1).

And the points are symmetry with respect to the point C.

Hence, the coordinates of C is the midpoint of the points A and B.

Determining coordinates of C using midpoint formula,

xm,ym=x1+x22,y1+y22

xm,ym are the midpoints and also the coordinate of C.

x1, y1=(3, -4)

x2, y2=(5, -1)

To determine

(b)

To find:

The coordinates of C given the points A (0, 2) and B 0, 6 and the points A and B are symmetry with respect to point C.

To determine

(c)

To find:

The coordinates of C given the points A (5, -3) and B (2, 1) and the points A and B are symmetry with respect to point C.

To determine

(d)

To find:

The coordinates of C given the points A 2a, 0and B0, 2b and the points A and B are symmetry with respect to point C.

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