Mathematics
The vertices of a Δ ABC are A(2, -3), B(-1, 2) and C(3, 0). This triangle is reflected in x-axis to form ΔA'B'C'. Find the co-ordinates of A', B' and C'. Are the two triangles congruent?
Reflection
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Answer
We know that,
Rule to find reflection of a point in x-axis :
Retain the abscissa i.e. x-coordinate.
Change the sign of ordinate i.e. y-coordinate.
∴ A(2, - 3) ⇒ A'(2, 3)
∴ B(-1, 2) ⇒ B'(-1, -2)
∴ C(3, 0) ⇒ C'(3, 0)
Yes, the two triangles are congruent. A reflection is an isometry, meaning it preserves distance and angle measure.
Therefore, Δ ABC ≅ ΔA'B'C'.
Hence, coordinates of the vertices of ΔA'B'C' are A'(2, 3), B'(-1, -2), C'(3, 0) and Δ ABC and ΔA'B'C' are congruent.
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