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Question
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
Options
y = x, y + x = 1
y = x, x + y = 2
2y = x, y + x = `1/3`
y = 2x, y + 2x = 1
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Solution
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are y = x, y + x = 1.
Explanation:
Given equation x = 0, y = 0
x = 1 and y = 1 form a square of side 1 unit
From figure, we get that OABC is square having corners O(0, 0), A(1, 0), B(1, 1) and C(0, 1)
Equation of diagonal AC
y – 0 = `(1 - 0)/(0 - 1) (x - 1)`
⇒ y = – (x – 1)
⇒ y = – x + 1
⇒ y + x = 1
Equation of diagonal OB is y – 0 = `(1 - 0)/(1 - 0) (x - 0)`
⇒ y = x
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