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Question
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
Options
(4, 3)
(3, 4)
(1, 4)
`7/2, 7/2`
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Solution
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are (3, 4).
Explanation:
Let the reflection of A(4, 1) in y = x be B(a, b) mid-point of AB
= `((4 + a)/2, (1 + b)/2)` which lies on y = x
⇒ `(4 + "a")/2 = (1 + b)/2`
⇒ 4 + a = 1 + b
⇒ a – b = – 3 .......(i)
The slope of the line y = x is 1 and slope of AB = `(b - 1)/(a - 4)`
∴ `1((b - 1)/(a - 4)) = - 1`
⇒ b – 1 = – a + 4
⇒ a + b = 5 ....(ii)
Solving equation (i) and equation (ii) we get
a = 1 and b = 4
∴ The point after translation is (1 + 2, 4) or (3, 4).
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