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?
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.
Related Questions
The point P(-6, -3) on reflection in y-axis is mapped on P'. The point P' on reflection in the origin is mapped on P".
(i) Find the co-ordinates of P'.
(ii) Find the co-ordinates of P".
(iii) Write down a single transformation that maps P onto P".
The point P(4, -7) is reflected in the origin to point P'. The point P' is then reflected in x-axis to the point P".
(i) Find the co-ordinates of P'.
(ii) Find the co-ordinates of P".
(iii) Write down a single transformation that maps P onto P".
The points P(-2, 4), Q(3, -1) and R(6, 2) are the vertices of a triangle. Δ PQR is reflected in y-axis to form ΔP'Q'R'. Find the co-ordinates of P', Q' and R'.
Use a graph paper for this question (Take 2 cm = 1 unit on both x and y axis).
(i) Plot the following points : A(0, 4), B(2, 3), C(1, 1) and D(2, 0)
(ii) Reflect points B, C, D on the y-axis and write down their co-ordinates. Name the images as B', C', D' respectively.
(iii) Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation of the line of symmetry of the figure formed.