Mathematics
(i) Name all the rays shown in the given figure whose initial point is A.
(ii) Is ray different from ray ?
(iii) Is ray different from ray ?
(iv) Is ray different from ray ?
(v) Is ray different from ray ?
Geometrical Concepts
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Answer
From the figure, the points lie on a line in the order E, A, B, C and D.
(i) Rays whose initial point is A — from A we can draw rays in two opposite directions on the line. Rays extend in one direction, and ray extends in the opposite direction.
∴ The rays with initial point A are .
(ii) Ray AB starts at A and goes in the direction of B. Ray AD also starts at A and goes in the same direction (through B and C to D). Since they have the same initial point and same direction, they are the same ray.
∴ Ray AB is not different from ray AD. They are the same ray.
(iii) Ray CA starts at C and goes in the direction of A. Ray CE also starts at C and goes in the same direction (through A to E). Since they have the same initial point and same direction, they are the same ray.
∴ Ray CA is not different from ray CE. They are the same ray.
(iv) Ray BA has initial point B and goes towards A. Ray CA has initial point C and goes towards A. Since their initial points are different, the rays are different.
∴ Yes, ray BA is different from ray CA.
(v) Ray ED has initial point E and extends in the direction of D. Ray DE has initial point D and extends in the direction of E (opposite direction). Since their initial points are different and they extend in opposite directions, they are different rays.
∴ Yes, ray ED is different from ray DE. They are opposite rays.
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