Mathematics
The triangle OAB is reflected in the origin O to triangle triangle OA'B'. A' and B' have coordinates (-3, -4) and (0, -5) respectively.
(i) Find the coordinates of A and B.
(ii) Draw a diagram to represent the given information.
(iii) What kind of figure is the quadrilateral ABA'B'?
(iv) Find the coordinates of A'', the reflection of A in the origin followed by reflection in the y-axis.
(v) Find the coordinates of B'', the reflection of B in the x-axis followed by the reflection in the origin.
Answer
The graph showing the given information is drawn below:
(i) Since, on reflection in the origin A becomes A'(-3, -4) and B becomes B'(0, -5) thus,
A = (3, 4) and B = (0, 5).
(iii) The quadrilateral ABA'B' represents a rectangle.
(iv) From graph we get,
The coordinates of A" is (3, -4).
(v) From graph we get,
The coordinates of B" is (0, 5).
Related Questions
A point P(a, b) become (-2, c) after reflection in the x-axis, and P becomes (d, 5) after reflection in the origin. Find the values of a, b, c and d.
A(4, -1), B(0, 7) and C(-2, 5) are the vertices of a triangle. △ABC is reflected in the y-axis and then reflected in the origin. Find the coordinates of the final images of the vertices.
The points A(4, -11), B(5, 3), C(2, 15) and D(1, 1) are the vertices of a parallelogram. If the parallelogram is reflected in the y-axis and then in the origin, find the coordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.
Use a graph paper for this question (take 2 cm = 1 unit on both x and y axes).
(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 y-axis and write down their coordinates. Name the images as B', C', D' respectively.
(iii) Join points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation of line of symmetry of the figure formed.