Question

the graph shows pentagons lm nop and lmnop. which of the following transformations maps lm nop onto lmnop? translation left 4 units and down 7 units translation left 7 units and down 4 units reflection across the x - axis reflection across the y - axis rotation 90° clockwise around the origin rotation 90° counterclockwise around the origin rotation 180° around the origin

Explanation:

Step1: Analyze translation

Check the change in x - and y - coordinates of corresponding vertices. For example, take vertex L( - 3,6). In L'( - 10,2), the x - coordinate changes from - 3 to - 10 (a change of - 7) and the y - coordinate changes from 6 to 2 (a change of - 4). This indicates a translation left 7 units and down 4 units.

Step2: Analyze reflection

For reflection across the x - axis, (x,y)→(x, - y). For reflection across the y - axis, (x,y)→( - x,y). The coordinates of the vertices do not follow these rules.

Step3: Analyze rotation

For 90° clockwise rotation around the origin (x,y)→(y, - x), for 90° counter - clockwise rotation (x,y)→( - y,x) and for 180° rotation (x,y)→( - x, - y). The coordinates of the vertices do not follow these rotation rules.

Answer:

translation left 7 units and down 4 units