Consider a triangle PQR with coordinates as P(0,0), Q(2,2) and R(10,4). If…
2023
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 :
- A.
(-20, -12) Q(-20, -4) and R(10,4)
- B.
(-30, -12) Q(-22, -4) and R(10,4)
- C.
(-25, -10) Q(22, -4) and R(10,4)
- D.
(30, -12) Q(-22, 4) and R(10,4)
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Correct answer: B
Key idea: perform a dilation with center at R(10,4) and scale factor 4.
Formula: For any point X, the image X' = R + 4*(X - R). This is algebraically X' = 4X - 3R.
Compute P': For P(0,0), P' = 4*(0,0) - 3*(10,4) = (0,0) - (30,12) = (-30,-12).
Compute Q': For Q(2,2), Q' = 4*(2,2) - 3*(10,4) = (8,8) - (30,12) = (-22,-4).
R stays fixed: R' = (10,4).
Final coordinates: P' = (-30,-12), Q' = (-22,-4), R' = (10,4).