Question

on a math test, nikoi needs to describe the motions which map △efg to △mno. the coordinates of △efg are e(6,3), f(8,3), and g(8,8). the coordinates of △mno are m(0,0), n(- 2,5), and o(- 2,8). she says there is a translation 6 units to the left and 3 units down, followed by a reflection across the x - axis. describe the sequence of motions. what is nikois likely error? which of the following is the description of the rigid motions which map △efg to △mno? a. a translation 5 units to the left and 2 units down, followed by a reflection across the y - axis b. a translation 6 units to the left and 3 units down, followed by a reflection across the y - axis c. a translation 6 units to the left and 3 units down, followed by a reflection across the x - axis

Explanation:

Step1: Analyze translation

Translation moves a figure. Moving $\triangle EFG$ 6 units left and 3 units down changes the x - coordinates by subtracting 6 and y - coordinates by subtracting 3.

Step2: Analyze reflection

Reflection flips a figure over a line. Reflecting over the x - axis changes the sign of the y - coordinate.

Step3: Check the options

For option A, the translation values are incorrect. For option B, the translation of 6 units left and 3 units down followed by reflection across the y - axis is wrong as reflection should be across x - axis. Option C has a translation of 6 units left and 3 units down followed by reflection across the x - axis which is correct.

Answer:

C. A translation 6 units to the left and 3 units down, followed by a reflection across the x - axis