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An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 9 to 9 in one unit increments. The y-axis ranges from negative 11 to 11 in one unit increments. Four points are plotted. A square is graphed using the four plotted points as vertices. Point A is plotted at coordinates left parenthesis 3 comma negative 4 right parenthesis. Point B is plotted at coordinates left parenthesis 7 comma negative 4 right parenthesis. Point C is plotted at coordinates left parenthesis 7 comma negative 8 right parenthesis. Point D is plotted at coordinates left parenthesis 3 comma negative 8 right parenthesis. Points A, B, C, and D are connected by solid lines to form square A B C D.

Reflect square ABCD
first across the x
-axis, and then across the y
-axis to create square A′B′C′D′
. What are the vertices of square A′B′C′D′
?

(1 point)
Responses

Square A′B′C′D′
has vertices A′(−3,4)
, B′(−7,4)
, C′(−7,8)
, and D′(−3,8)
.
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 3 comma 4 right parenthesis , upper B prime left parenthesis negative 7 comma 4 right parenthesis , upper C prime left parenthesis negative 7 comma 8 right parenthesis , and upper D prime left parenthesis negative 3 comma 8 right parenthesis .

Square A′B′C′D′
has vertices A′(3,4)
, B′(7,4)
, C′(7,8)
, and D′(3,8)
.
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis 3 comma 4 right parenthesis , upper B prime left parenthesis 7 comma 4 right parenthesis , upper C prime left parenthesis 7 comma 8 right parenthesis , and upper D prime left parenthesis 3 comma 8 right parenthesis .

Square A′B′C′D′
has vertices A′(−3,−4)
, B′(−7,−4)
, C′(−7,−8)
, and D′(−3,−8)
.
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 3 comma negative 4 right parenthesis , upper B prime left parenthesis negative 7 comma negative 4 right parenthesis , upper C prime left parenthesis negative 7 comma negative 8 right parenthesis , and upper D prime left parenthesis negative 3 comma negative 8 right parenthesis .

Square A′B′C′D′
has vertices A′(−3,4)
, B′(−7,4)
, and C′(−7,8)
.
Square upper A prime upper B prime upper C prime upper D prime has vertices upper A prime left parenthesis negative 3 comma 4 right parenthesis , upper B prime left parenthesis negative 7 comma 4 right parenthesis , and upper C prime left parenthesis negative 7 comma 8 right parenthesis .
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1 answer

To find the vertices of square A'B'C'D' after reflecting square ABCD first across the x-axis and then across the y-axis, we follow these steps:

  1. Reflect across the x-axis:

    • The x-coordinate stays the same.
    • The y-coordinate changes sign.

    For the original points:

    • A(3, -4) becomes A'(3, 4)
    • B(7, -4) becomes B'(7, 4)
    • C(7, -8) becomes C'(7, 8)
    • D(3, -8) becomes D'(3, 8)

    So after reflecting across the x-axis, the new points are:

    • A'(3, 4)
    • B'(7, 4)
    • C'(7, 8)
    • D'(3, 8)

  2. Reflect across the y-axis:

    • The x-coordinate changes sign.
    • The y-coordinate stays the same.

    For the new points after the x-axis reflection:

    • A'(3, 4) becomes A''(-3, 4)
    • B'(7, 4) becomes B''(-7, 4)
    • C'(7, 8) becomes C''(-7, 8)
    • D'(3, 8) becomes D''(-3, 8)

    Hence, the final coordinates for square A'B'C'D' are:

    • A''(-3, 4)
    • B''(-7, 4)
    • C''(-7, 8)
    • D''(-3, 8)

So the correct response is: Square A′B′C′D′ has vertices A′(−3, 4), B′(−7, 4), C′(−7, 8), and D′(−3, 8).