Q11.Marks: +2.0UGC NET Paper 2: Computer Science 7th Dec 2023 Shift 2
Consider a triangle PQR with coordinates as P(0,0), Q(2,2) and R(10,4). If this triangle is to be magnified to four times its size while keeping R(10, 4) fixed, then the coordinates of the magnified triangle are :
1.(-20, -12), Q(-20, -4) and R(10, 4)
2.(-30, -12), Q(-22, -4) and R(10, 4)✓ Correct
3.(-25, -10), Q(22, -4) and R(10, 4)
4.(30,-12), Q(-22, 4) and R(10, 4)
Solution
The correct answer is (-30, -12), Q(-22, -4) and R(10, 4)
EXPLANATION:
To magnify a shape, we can use the principle of scalings in transformations. We keep the point R(10,4) fixed and magnify everything with a factor of 4 from that point.
Start with thepoint P(0,0).
The vector from R to P is P - R = (0,0) - (10,4) = (-10, -4). Now, we multiply this vector by 4 (our scale factor) to get (-40, -16). Then, we add this to our fixed point R, to get the new position for P: R + 4*(P - R) = (10,4) + (-40, -16) = (-30, -12).
Similarly, for point Q(2,2).
The vector from R to Q is Q - R = (2,2) - (10,4) = (-8, -2). Again, we multiply this vector by our scale factor 4, to get (-32, -8). Adding this to R, we find the new position for Q: R + 4*(Q - R) = (10,4) + (-32, -8) = (-22, -4).
The coordinates of the magnified triangle are thus P'(-30, -12), Q'(-22, -4) and R(10, 4).
So, option 2) (-30, -12), Q(-22, -4) and R(10, 4) is the correct one.