Question

fluency
point reflections
n-gen math geometry homework
date

1. a point reflection across point c is equivalent to which of the following?

(1) a ( 90^{circ} ) rotation about point c
(2) a ( 180^{circ} ) rotation about point c
(3) a ( 270^{circ} ) rotation about point c
(4) a ( 360^{circ} ) rotation about point c

1. in the diagram shown, ( overline{q r} ) is the image of ( overline{m n} ) after a point reflection across point p. which of the following does not have to be true?

(1) ( overline{m n} cong overline{q r} )
(2) ( overline{m p} cong overline{q p} )
(3) ( overline{p n} cong overline{p r} )
(4) ( overline{m p} cong overline{r p} )

1. given ( overline{w x} ) containing point l, if ( overline{w x} ) is reflected across point l to produce ( overline{w^{prime} x^{prime}} ), then which of the following is true about ( overline{w x} ) and ( overline{w^{prime} x^{prime}} )?

(1) they are parallel
(2) they are perpendicular
(3) they are the same line
(4) they intersect only once at l

1. if the point ( t(-3,7) ) is reflected across the origin, then its image has coordinates

(1) ( t^{prime}(3,-7) )
(2) ( t^{prime}(3,7) )
(3) ( t^{prime}(7,-3) )
(4) ( t^{prime}(-7,3) )

1. if ( overline{g h} ) is rotated ( 180^{circ} ) about point m, and point m does not lie on ( overline{g h} ), then which of the following is true about ( overline{g h} ) and its image ( overline{g^{prime} h^{prime}} )?

(1) ( overline{g h} cong overline{g^{prime} h^{prime}} ) and ( overline{g h} | overline{g^{prime} h^{prime}} )
(2) ( overline{g h} cong overline{g^{prime} h^{prime}} ) and ( overline{g h} perp overline{g^{prime} h^{prime}} )
(3) ( overline{g h} ) and ( overline{g^{prime} h^{prime}} ) are the same segment
(4) m is the midpoint of both ( overline{g h} ) and ( overline{g^{prime} h^{prime}} )

Explanation:

1.

A point reflection across a point is equivalent to a \(180^{\circ}\) rotation about that point.

2.

By the property of point reflection, \(MN\cong QR\), \(MP\cong QP\), \(PN\cong PR\). But \(MP\) is not congruent to \(RP\).

3.

When a line segment is reflected across a point \(L\) on it, the original line segment \(\overline{WX}\) and its image \(\overline{W'X'}\) are the same line.

4.

The rule for reflecting a point \((x,y)\) across the origin is \((x,y)\to(-x,-y)\). For the point \(T(-3,7)\), \(x = - 3\), \(y = 7\), so its image is \(T'(3,-7)\).

5.

When a line segment \(\overline{GH}\) is rotated \(180^{\circ}\) about a point \(M\) (not on \(\overline{GH}\)), \(\overline{GH}\cong\overline{G'H'}\) and \(\overline{GH}\parallel\overline{G'H'}\).

Answer:

1. (2)
2. (4)
3. (3)
4. (1)
5. (1)