Question

Original point Translated point
D (-3, 4) D
′
(-7, 3)
E (2, 8) E
′
(-2, 7)
F (1, -6) F
′
(-3, -7)



Compared to the original point, the x-coordinate of the translated point
by
, and the y-coordinate of the translated point
b

Answer 1

To find the changes in the x-coordinates and y-coordinates from the original points to the translated points, we can analyze each point pair.

### D to D':
- Original point D: (-3, 4)
- Translated point D': (-7, 3)

**Change in x-coordinate:**
- \(-7 - (-3) = -7 + 3 = -4\)

**Change in y-coordinate:**
- \(3 - 4 = -1\)

### E to E':
- Original point E: (2, 8)
- Translated point E': (-2, 7)

**Change in x-coordinate:**
- \(-2 - 2 = -4\)

**Change in y-coordinate:**
- \(7 - 8 = -1\)

### F to F':
- Original point F: (1, -6)
- Translated point F': (-3, -7)

**Change in x-coordinate:**
- \(-3 - 1 = -4\)

**Change in y-coordinate:**
- \(-7 - (-6) = -7 + 6 = -1\)

### Summary of Changes:
From the analysis above, we find that:
- The change in the x-coordinate (a) is \(-4\) for all points (D, E, F).
- The change in the y-coordinate (b) is \(-1\) for all points (D, E, F).

Thus, we conclude:
- \(a = -4\)
- \(b = -1\)