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How do you perform a reflection of a triangle over the y-axis?

To reflect a triangle over the y-axis, you need to change the sign of the x-coordinates of its vertices.

When you perform a reflection of a triangle across the y-axis, you create a mirror image of the triangle on the opposite side of the y-axis. This process involves taking each vertex (corner) of the triangle and inverting its x-coordinate while keeping the y-coordinate unchanged.

For instance, consider a triangle with vertices A(2,3)A(2, 3), B(4,5)B(4, 5), and C(6,1)C(6, 1). To reflect these points over the y-axis, you would change the x-coordinates to their negatives. Therefore, the reflected vertices would be A(2,3)A'(-2, 3), B(4,5)B'(-4, 5), and C(6,1)C'(-6, 1).

This transformation can be expressed mathematically as (x,y)(x,y)(x, y) \rightarrow (-x, y). By applying this rule to each vertex of the triangle, you ensure that the shape and size of the triangle remain unchanged, while its position is mirrored across the y-axis. This technique is particularly useful in various geometric problems and enhances your understanding of symmetry and transformations in coordinate geometry.

Answered by: Dr. Emily Clark
GCSE Maths Tutor
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