Question

the graph shows triangles wxy and wxy. which sequence of transformations maps wxy onto wxy? a translation left 8 units and up 3 units followed by a reflection across the x - axis a rotation 180° around the origin followed by a translation left 4 units and down 3 units a reflection across the y - axis followed by a rotation 90° clockwise around the origin

Explanation:

Step1: Recall transformation rules

Translation moves a figure, rotation turns it around a point, and reflection flips it over a line.

Step2: Analyze option 1

A translation left 8 units and up 3 units followed by reflection across x - axis won't map correctly as orientation and position won't match.

Step3: Analyze option 2

For a rotation of 180° around the origin, the rule is (x,y)→(-x,-y). Then a translation left 4 units (subtract 4 from x - coordinate) and down 3 units (subtract 3 from y - coordinate). Let's assume a point (x,y) on △WXY. After 180° rotation it becomes (-x,-y), then after translation it becomes (-x - 4,-y - 3). This sequence maps △WXY onto △W'X'Y'.

Step4: Analyze option 3

A reflection across the y - axis (x,y)→(-x,y) followed by 90° clockwise rotation (x,y)→(y,-x) won't map the triangle correctly.

Answer:

a rotation 180° around the origin followed by a translation left 4 units and down 3 units