Question

the graph shows rectangles defg and defg. which of the following transformations maps defg onto defg? translation left 7 units and up 5 units translation left 13 units and up 2 units reflection across the x - axis reflection across the y - axis

Explanation:

Step1: Analyze x - coordinate change

Let's take a point, say point D(7,1). In D'E'F'G', the corresponding point D' has coordinates (- 6,6). The change in the x - coordinate is \(\Delta x=-6 - 7=-13\) (a shift of 13 units to the left).

Step2: Analyze y - coordinate change

The change in the y - coordinate of point D is \(\Delta y=6 - 1 = 5\) (a shift of 5 units up).

Step3: Check each option

• For a translation left 7 units and up 5 units, the x - coordinate change should be - 7 and y - coordinate change should be 5. But we found \(\Delta x=-13\).
• For a translation left 13 units and up 5 units, \(\Delta x=-13\) and \(\Delta y = 5\) which matches our calculations.
• For a reflection across the x - axis, the sign of the y - coordinate of each point would change. But the y - coordinates of the points in D'E'F'G' are not the negative of the y - coordinates of the points in DEFG.
• For a reflection across the y - axis, the sign of the x - coordinate of each point would change. But the x - coordinates of the points in D'E'F'G' are not the negative of the x - coordinates of the points in DEFG.

Answer:

translation left 13 units and up 5 units