Question

which point is a reflection of point p in the mirror line marked m? image of a coordinate grid with point p and points a, b, c, d; multiple choice options a, d, b, c

Explanation:

Step1: Recall reflection over vertical line

For a vertical mirror line \( m \), the reflection of a point \( (x,y) \) will have a horizontal distance from \( m \) equal to the original point's horizontal distance, but on the opposite side. Also, the \( y \)-coordinate remains the same (since it's a vertical reflection, vertical position doesn't change).

Step2: Analyze point P's position

Point \( P \) is on a vertical dashed line. Let's count the number of vertical intervals (dashed lines) from \( P \) to mirror line \( m \). Then, the reflected point should be the same number of intervals on the other side of \( m \), with the same \( y \)-coordinate (same horizontal row, since vertical reflection preserves \( y \)-coordinate for vertical lines).

Looking at the points:

• Point \( B \): Check the horizontal distance from \( m \) and \( y \)-coordinate. The \( y \)-coordinate of \( P \) and \( B \) is the same (they are on the same horizontal line). The number of vertical dashed - line intervals from \( P \) to \( m \) and from \( m \) to \( B \) is equal.
• Point \( A \): Different \( y \)-coordinate, so not a reflection.
• Point \( D \): Different \( y \)-coordinate, so not a reflection.
• Point \( C \): The horizontal distance from \( m \) is not equal to that of \( P \) (or \( y \)-coordinate match but distance wrong).

Answer:

B