Question: The quadrilateral ABCD has the vertices A(3, 4), B(5, 4), C(5, 2), D(3, 2). The mirror line is at x = 0.
Identify the perpendicular distance for each coordinate to the mirror line.
B and C are 3 units.
A and D are 5 units.
A and C are 3 units.
B and D are 5 units.
A and D are 3 units.
B and C are 5 units.
A and B are 3 units.
C and D are 5 units.
graph: quadrilateral ABCD is shown by the coordinates A(3,4), B(5,4), C(5,2), and D(3,2) in the center-right; the mirror line is x = 0 on the left side of the coordinate plane, position_hint=center
User: help with this
1. **State the problem:** We need to find the perpendicular distance from each vertex of quadrilateral ABCD to the mirror line at $$x=0$$.
2. **Recall the formula for distance from a point to a vertical line:** The distance from a point $$(x,y)$$ to the vertical line $$x = k$$ is $$|x - k|$$.
3. **Apply the formula to each vertex:**
- For $$A(3,4)$$, distance to $$x=0$$ is $$|3 - 0| = 3$$ units.
- For $$B(5,4)$$, distance to $$x=0$$ is $$|5 - 0| = 5$$ units.
- For $$C(5,2)$$, distance to $$x=0$$ is $$|5 - 0| = 5$$ units.
- For $$D(3,2)$$, distance to $$x=0$$ is $$|3 - 0| = 3$$ units.
4. **Summarize the distances:**
- Points $$A$$ and $$D$$ are each $$3$$ units from the mirror line.
- Points $$B$$ and $$C$$ are each $$5$$ units from the mirror line.
5. **Match with the given options:** The correct option is:
$$\text{A and D are 3 units.}\\\text{B and C are 5 units.}$$
**Final answer:** A and D are 3 units; B and C are 5 units from the mirror line $$x=0$$.