Question

Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral A'B'C'D'. The coordinates of A' are ( , ).

The reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A''B''C''D''. The coordinates of A'' are ( , ).

For A', you provided the coordinates (-5, 3) as the result of the reflection across the x-axis.

For A'', you provided the coordinates (-2, 5) as the result of translating A' 3 units to the right and 2 units up.

Please note that the missing values for the coordinates are not provided, so you may need to fill in the blanks with the appropriate values.

Answer 1

The question involves applying geometric transformations to a point in a quadrilateral. The student correctly reflected and translated a point, switching from (-5, -3) to (-5, 3), and then to (-2, 5) respectively.

Step-by-step explanation:

The subject matter is a mathematical transformation that involves a reflection across the x-axis and a subsequent translation. When reflecting point A across the x-axis, if the original point A had coordinates (a, b), then the reflected point A' will have coordinates (a, -b), since reflection across the x-axis inverts the sign of the y-coordinate. In the case for point A', the student provided the reflected coordinates as (-5, 3). This means the original coordinates of point A were (-5, -3).

Next, translating a point involves shifting it by a certain number of units horizontally, vertically, or both. For point A', a translation 3 units to the right increases the x-coordinate by 3. Likewise, a translation 2 units up increases the y-coordinate by 2. Therefore, starting from the reflected coordinates (-5, 3) of point A', the translated coordinates A'' become (-5 + 3, 3 + 2), which simplifies to (-2, 5).