Straight LineHardBloom L3
Question
In the figure shown, $OABC$ is a rectangle with dimensions $OA = 3$ units and $OC = 4$ units. If $AD = 1.5$ units then slope of diagonal $OB$ will be:
Options
A.$\frac{1}{\sqrt{2}}$
B.$\frac{\sqrt{2}}{\sqrt{3}}$
C.$\frac{1}{2}$
D.$\frac{1}{3}$
Solution
Sol. [Key Concept: Use the rectangle's dimensions and the tangent of the diagonal's inclination to get the slope of $OB$.]
$$tan\theta = \frac{3}{4},tan\phi = \frac{3}{2(3)} = \frac{1}{2} $$
$$\begin{matrix} \text{~}\text{slope of}\text{~}OB & \ = \tan\left( \frac{\pi}{2} - (\theta + \phi) \right) = \cot(\theta + \phi) \\ & \ = \frac{1 - \frac{3}{4} \cdot \frac{1}{2}}{\frac{3}{4} + \frac{1}{2}} = \frac{1}{2} \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
Let the line L pass through the point $( - 3,5,2)$ and make equal angles with the positive coordinate axes. If the dista...If the slope of a line is 2 and it cuts an intercept − 4 on y-axis, then its equation will be -...Find the fix point through which the line x(a + 2b) + y (a + 3b) = a + b always passes for all values of a and b -...Let $A(1,0),B(2, - 1)$ and $C\left( \frac{7}{3},\frac{4}{3} \right)$ be three points. If the equation of the bisector of...If the points where the lines $3x - 2y - 12 = 0$ and $x + ky + 3 = 0$ intersect both the coordinate axes are concyclic, ...