Triangle `OA_(1)B_(1)` is the reflection of triangle OAB in origin, where `A_(1) (4, -5)` is the image of A and `B_(1) (-7, 0)` is the image of B.
Find the co-ordinates of `B_(2)`, the image of B under reflection in y-axis followed by reflection in origin.

Answer

To find the coordinates of \( B_2 \), the image of \( B \) under reflection in the y-axis followed by reflection in the origin, we can follow these steps:

### Step 1: Find the coordinates of point \( B \)
Given that \( B_1(-7, 0) \) is the image of point \( B \) after reflection in the origin, we can find the coordinates of \( B \) by reflecting \( B_1 \) back through the origin.

The formula for reflection through the origin is:
\[ (x, y) \rightarrow (-x, -y) \]

Applying this to \( B_1(-7, 0) \):
\[ B = (-(-7), -0) = (7, 0) \]

### Step 2: Reflect point \( B \) in the y-axis
To find the image of point \( B \) under reflection in the y-axis, we use the reflection formula:
\[ (x, y) \rightarrow (-x, y) \]

Applying this to \( B(7, 0) \):
\[ B' = (-7, 0) \]

### Step 3: Reflect point \( B' \) in the origin
Now, we need to reflect \( B'(-7, 0) \) through the origin again using the same reflection formula:
\[ (x, y) \rightarrow (-x, -y) \]

Applying this to \( B'(-7, 0) \):
\[ B_2 = (-(-7), -0) = (7, 0) \]

### Final Answer
Thus, the coordinates of \( B_2 \) are \( (7, 0) \).

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