Question

What is the length of
BC
undergoes a reflection over the y-axis ?

b=5,2
c=2,2

Answer 1

To find the length of segment \( BC \) after it undergoes a reflection over the y-axis, we first need to determine the coordinates of points \( B \) and \( C \).

Given the points:
- \( B(5, 2) \)
- \( C(2, 2) \)

### Step 1: Reflect the Points Over the y-axis

The reflection of a point \( (x, y) \) over the y-axis is given by \( (-x, y) \). Therefore:

- The reflection of point \( B(5, 2) \) is \( B'(-5, 2) \).
- The reflection of point \( C(2, 2) \) is \( C'(-2, 2) \).

### Step 2: Calculate the Length of Segment \( B'C' \)

Now we need to determine the length of segment \( B'C' \). The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting in the coordinates of \( B' \) and \( C' \):

- \( B'(-5, 2) \)
- \( C'(-2, 2) \)

The length \( B'C' \) can be calculated as follows:

\[
d = \sqrt{((-2) - (-5))^2 + (2 - 2)^2}
\]
\[
= \sqrt{(-2 + 5)^2 + 0^2}
\]
\[
= \sqrt{(3)^2}
\]
\[
= \sqrt{9}
\]
\[
= 3
\]

### Conclusion

The length of segment \( BC \), after undergoing a reflection over the y-axis, is **3 units**.