Question

A coordinate plane shows a translation of a line segment. The original line segment is AB. The coordinates of the endpoints are A at (4, negative 2) and B at (12, negative 4). The translated line segment is A prime B prime. The coordinates of the endpoints are A prime at (1, 0) and B prime at (3, negative 1). The translation appears to be 3 units to the left and 2 units up.

Image Long DescriptionThe graph displays two distinct line segments plotted on a coordinate plane. The x-axis ranges from 0 to 13, while the y-axis spans from negative 5 to 0. The first line segment, labeled Upper A Upper B, begins at point Upper A with coordinates left parenthesis 4 comma negative 2 right parenthesis and extends to point Upper B at left parenthesis 12 comma negative 4 right parenthesis. This segment slopes downward as it moves from left to right. The second line segment, labeled Upper A prime Upper B prime, starts at point Upper A prime with coordinates left parenthesis 1 comma negative 0.5 righ
A′B′¯¯¯¯¯¯¯¯¯¯
𝐴
′
𝐵
′
¯
passes through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
.
line segment upper A prime upper B prime passes through the center of dilation because it is taken to a line parallel to line segment upper A upper B .

A′B′¯¯¯¯¯¯¯¯¯¯
𝐴
′
𝐵
′
¯
does not pass through the center of dilation because it is taken to a line parallel to AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
.
line segment upper a prime upper b prime does not pass through the center of dilation because it is taken to a line parallel to line segment upper A upper b .

A′B′¯¯¯¯¯¯¯¯¯¯
𝐴
′
𝐵
′
¯
passes through the center of dilation because it is an enlargement of AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
by a scale factor of 4.
line segment upper A prime upper b prime passes through the center of dilation because it is an enlargement of line segment upper A upper b by a scale factor of 4.

A′B′¯¯¯¯¯¯¯¯¯¯
𝐴
′
𝐵
′
¯
does not pass through the center of

Answer 1

There are some inconsistencies in the coordinates as written. I’ll check the key facts and show why the stated “translation 3 left and 2 up” can’t be correct for both endpoints.

1. Translation vector from A to A':
- A = (4, −2)
- A' = (1, 0)
Delta = A' − A = (1−4, 0−(−2)) = (−3, +2).

2. Translation vector from B to B':
- B = (12, −4)
- B' = (3, −1)
Delta = B' − B = (3−12, −1−(−4)) = (−9, +3).

Because the two deltas are different, AB → A'B' is not a single rigid translation. A single translation requires the same vector for both endpoints.

3. Check parallelism (slope):
- slope(AB) = (−4 − (−2)) / (12 − 4) = (−2)/8 = −1/4.
- slope(A'B') = (−1 − 0) / (3 − 1) = −1/2.

Slopes are different, so A'B' is not parallel to AB.

4. Check scale/ dilation possibility (quick check of lengths):
- |AB| = sqrt(8^2 + (−2)^2) = sqrt(68) ≈ 8.246.
- |A'B'| = sqrt(2^2 + (−1)^2) = sqrt(5) ≈ 2.236.
The ratio ≈ 0.271, but because the endpoints do not line up in direction (not parallel) a simple dilation about any single center is not consistent.

Conclusion
- The transformation is not the uniform translation (−3, +2) for both points.
- A'B' is not parallel to AB.
- There is no single dilation (about one center) taking AB to A'B' as described.

If some coordinates were mistyped (for example A' = (1, −0.5) appears in your pasted text), tell me the intended coordinates and I’ll re-evaluate and pick the correct statement(s). If you want to choose among given answer choices, paste them cleanly and I’ll mark which are true.