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Question

The angle between the line joining the points 1,-2,3,2 and the line x+2y-7=0 is


A

π

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B

π2

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C

π3

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D

π6

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Solution

The correct option is B

π2


Explanation for the correct option:

Step 1: Finding the equation for two point form of line

The two point form of line is expressed as

y-y1=y2-y1x2-x1x-x1

The line joining the points are 1,-2,3,2

y+2=2+23-1x-1y+2=42x-1y+2=2x-1y+2=2x-22x-y-4=0

Step 2: Finding the slope

Slope of the Equation is Coefficient of x and coefficient of y

m1=-2-1=2

Consider the given Equation as,

x+2y-7=0

Slope of the Equation is Coefficient of x and coefficient of y

m2=-12

Step 3: Finding the angle between the line

Then,

m1×m2=2×-12=-1

Thus, m1 perpendicular to m2 and the angle between the two lines equal to π2or90°

Hence, option (B) is the correct answer.


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