Angle made by the line y = x with the positive direction of X – axis

1.	Angle made by the line y = x with the positive direction of X – axis is A) 80°B) 45° C) 90° D) 100°
Answer» Correct option is (B) 45° Let \(\theta\) be the angle made by the line y = x with the positive direction of X-axis. Then slope of line is \(m=tan\,\theta.\) Given line is y = x. By comparing with slope-intercept form of line (i.e., y = mx), we get m = 1. But slope of line is \(m=tan\,\theta.\) \(\therefore\) \(tan\,\theta=1=tan\;45^\circ\) \(\Rightarrow\) \(\theta=45^\circ\) Hence, angle made by the line y = x with the positive direction of X-axis is \(45^\circ.\) Correct option is B) 45°

Angle made by the line y = x with the positive direction of X – axis is A) 80°B) 45° C) 90° D) 100°

Answer»

Correct option is (B) 45°

Let \(\theta\) be the angle made by the line y = x with the positive direction of X-axis. Then slope of line is \(m=tan\,\theta.\)

Given line is y = x.

By comparing with slope-intercept form of line (i.e., y = mx), we get m = 1.

But slope of line is \(m=tan\,\theta.\)

\(\therefore\) \(tan\,\theta=1=tan\;45^\circ\)

\(\Rightarrow\) \(\theta=45^\circ\)

Hence, angle made by the line y = x with the positive direction of X-axis is \(45^\circ.\)

Correct option is B) 45°

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