Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is:
Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is:
Option 1 -
(11/5, 28/5)
Option 2 -
(29/5, 8/5)
Option 3 -
(8/5, 29/5)
Option 4 -
(29/5, 11/5)
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:Equation of line is x/3 + y/1 = 1
⇒ x + 3y - 3 = 0
The image (x? , y? ) of point (-1, -4) is given by:
(x? - (-1)/1 = (y? - (-4)/3 = -2 (1 (-1) + 3 (-4) - 3) / (1² + 3²)
(x? + 1)/1 = (y? + 4)/3 = -2 (-1 - 12 - 3)/10 = -2 (-16)/10 = 16/5
x? + 1 = 16/5 ⇒ x? = 11/5
(y? + 4)/3 = 16/5 ⇒ y? + 4 = 48/5 ⇒ y? = 28/5
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