The straight lines $x + y = 1$ and $x - y = 5$ are perpendicular to each other.

True

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False

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Solution

The correct option is A True
Given the lines are $x + y = 1$ .......(1) and $x - y = 5$ ......(2).
Equation (1) and (2) can be written as $y = 1 - x$ and $y = - 5 + x$ .
The slope of line (1) is $- 1$ and that of the second line is $1$ .
Their product ot slope is $- 1.1 = - 1$ .
So they are perpendicular to each other.

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The straight lines x+y=1 and x−y=5 are perpendicular to each other.

The correct option is A TrueGiven the lines are x+y=1.......(1) and x−y=5......(2).Equation (1) and (2) can be written as y=1−x and y=−5+x.The slope of line (1) is −1 and that of the second line is 1.Their product ot slope is −1.1=−1.So they are perpendicular to each other.

The straight lines $x + y = 1$ and $x - y = 5$ are perpendicular to each other.