A, B and C are the points on a coordinate plane. The $Δ A B C$ is a right-angled triangle (right-angled at C ). If $A C$ is parallel to the X-axis and the angle between $A B$ and $A C$ is $45^{o}$ . The slope of $A B$ is___ .

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$\sqrt{2}$

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not defined

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Solution

The correct option is B
1

If $θ$ is the angle made by a line with the positive X-direction then the slope of the line is given by $T a n θ$ .

Here, $A C$ is parallel to X-axis. If a line makes an angle $θ$ with $A C$ then, the angle made by the line with X-axis is $θ$ .

So, the slope of $A B = T a n (45^{o}) = 1$ .

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A, B and C are the points on a coordinate plane. The ΔABC is a right-angled triangle (right-angled at C ). If AC is parallel to the X-axis and the angle between AB and AC is 45o. The slope of AB is___ .

The correct option is B 1 If θ is the angle made by a line with the positive X-direction then the slope of the line is given by Tanθ. Here, AC is parallel to X-axis. If a line makes an angle θ with AC then, the angle made by the line with X-axis is θ. So, the slope of AB=Tan(45o)=1.

A, B and C are the points on a coordinate plane. The $Δ A B C$ is a right-angled triangle (right-angled at C ). If $A C$ is parallel to the X-axis and the angle between $A B$ and $A C$ is $45^{o}$ . The slope of $A B$ is___ .