Question

The angle between the lines x + 2y = 5 and 2x – y + 7 = 0 is​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The angle between the given lines is 90°

Step-by-step explanation:

Given equations are:

x + 2y = 5

=> 2y = -x + 5

=> y = $\frac{-x}{2}$ + $\frac{5}{2}$                   --(i)

2x - y + 7 = 0

=> y = 2x + 7                 --(ii)

We know that equation of a line is y = mx + c        --(iii)

where m is the slope of the line

Comparing equation (i) with equation (iii)

Slope of line 1 = -1/2

Comparing equation (ii) with equation (iii)

Slope of line 2 = 2

We know that the lines are perpendicular to each other if the product of slopes of these lines is -1

Multiplying the slopes of line 1 and line 2, we get,

-(1/2) * 2 = -1

As the product of slopes of lines is -1,

=> they are perpendicular to each other

=> the angle between the given lines is 90°