Question

HELP ITS HARD Which statement is true about figures ABCD and A'B'C'D'? A polygon ABCD has A at ordered pair negative 4, negative 3, B at negative 3, negative 1, C at negative 2 and negative 3, D at negative 3 and negative 4. A polygon A prime B prime C prime D prime has A prime at ordered pair 3, 4, B prime at ordered pair 1, 3, C prime at ordered pair 3, 2, and D prime at ordered pair 4, 3. A'B'C'D' is obtained by translating ABCD 4 units up and then reflecting it about the y-axis. A'B'C'D' is obtained by translating ABCD 4 units right and then reflecting it about the x-axis. A'B'C'D' is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it about the y-axis. A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.

Answer 1

A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.

Explanation:

ABCD: A(-4,-3), B(-3,-1), C(-2,-3), and D(-3,-4).

If we rotate ABCD counterclockwise by 90 degrees, we obtain the translation

This gives:

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

Next, we reflect A''B''C''D'' across the x-axis. (Note that the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.)

This then gives us the coordinates

A'B'C'D': A'(3, 4), B'(1, 3), C'(3, 2), and D'(4, 3)

Answer 2

A'B'C'D' is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.

Explanation:

ABCD: A(-4,-3), B(-3,-1), C(-2,-3), and D(-3,-4).

If we rotate ABCD counterclockwise by 90 degrees, we obtain the translation

`R$otation of 90\º: (x,y)\rightarrow (-y,x)`

This gives:

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

Next, we reflect A''B''C''D'' across the x-axis. (Note that the x-coordinate remains the same, but the y-coordinate is transformed into its opposite.)

`R$eflection accross the x-axis: (x,y)\rightarrow (x,-y)`

This then gives us the coordinates

A'B'C'D': A'(3, 4), B'(1, 3), C'(3, 2), and D'(4, 3)