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Maths-

General

Easy

Question

The angle between the line x + y = 1 and x – y = 2 is

90°
30°
45°
1°

hint Hint:

First, we will find the slopes of the lines. The slope of a line $a x plus b y plus c equals 0$ is given by $m equals fraction numerator negative c o e f f i c i e n t space o f space x over denominator c o e f f i c i e n t space o f space y end fraction$ . After that we will use the formula of the angle between the two lines $tan open parentheses theta close parentheses equals open vertical bar fraction numerator m subscript 1 minus m subscript 2 over denominator 1 plus m subscript 1 m subscript 2 end fraction close vertical bar$ where $m subscript 1$ and $m subscript 2$ are the slope of the lines and $theta$ is the angle between the lines.

The correct answer is: 90°

The formula of the angle between the two lines is given by $tan open parentheses theta close parentheses equals open vertical bar fraction numerator m subscript 1 minus m subscript 2 over denominator 1 plus m subscript 1 m subscript 2 end fraction close vertical bar$ where $m subscript 1$ and $m subscript 2$ are the slope of the lines and $theta$ is the angle between the lines.
Step1: Finding the Slopes of the lines.
The slope of a line $a x plus b y plus c equals 0$ is given by $m equals fraction numerator negative c o e f f i c i e n t space o f space x over denominator c o e f f i c i e n t space o f space y end fraction$ hence, $m equals fraction numerator negative b over denominator a end fraction$ .
Therefore slopes of the given lines are $m subscript 1 equals negative 1$ and $m subscript 2 equals 1$
Step2: Finding the angles between the lines.
$tan open parentheses theta close parentheses equals open vertical bar fraction numerator m subscript 1 minus m subscript 2 over denominator 1 plus m subscript 1 m subscript 2 end fraction close vertical bar$
=> $tan open parentheses theta close parentheses equals open vertical bar fraction numerator negative 1 minus 1 over denominator 1 plus left parenthesis negative 1 right parenthesis cross times 1 end fraction close vertical bar$
=> $tan open parentheses theta close parentheses equals open vertical bar fraction numerator negative 2 over denominator 0 end fraction close vertical bar$
=>Since, the denominator is zero the value of $tan open parentheses theta close parentheses$ goes to infinity.
=>The value of $theta$ will be $90 to the power of ring operator$ .

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