Points A B are in the first quadrant ; point 'O' is the origin. If the slope of OA is 1 , slope of OB is 7 and OA = OB, then the slope of AB is -

Question

Points A B are in the first quadrant ; point 'O' is the origin. If the slope of OA is 1 , slope of OB is 7 and OA = OB, then the slope of AB is - (A) -1 / 5 (B) -1 / 4 (C) -1 / 3 (D) -1 / 2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2db70f8925c911aa380866e01bc33749-.png" /> m OA =1, m OB =7 Let m AB = m AO = OB ⇒ angle OBA = angle OAB ( m -7/1+7 m )=(1- m /1+ m ) ⇒ m =-(1/2), 2 but slope of A B is negative ∴ m=-(1/2)

Q. Points $A & B$ are in the first quadrant ; point ' $O$ ' is the origin. If the slope of $O A$ is $1$ , slope of $OB$ is $7$ and $O A = OB$ , then the slope of $A B$ is -

$- 1/5$

$- 1/4$

$- 1/3$

$- 1/2$

$m_{O A} = 1, m_{OB} = 7$
Let $m_{A B} = m$
$A O = OB$
$\Rightarrow ∠ OB A = ∠ O A B$
$\frac{m - 7}{1 + 7 m} = \frac{1 - m}{1 + m} \Rightarrow m = - \frac{1}{2}, 2$
but slope of $A B$ is negative
$∴ m = - \frac{1}{2}$

Q. Points A&B are in the first quadrant ; point 'O' is the origin. If the slope of OA is 1 , slope of OB is 7 and OA=OB, then the slope of AB is -

−1/5

−1/4

−1/3

−1/2