Two equal sides of an isosceles triangle are along – x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum, of all possible distinct values of m, is: [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Two equal sides of an isosceles triangle are along – x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum, of all possible distinct values of m, is: [2025]

1 $- 2 \sqrt{10}$

2 12

3 –6

4 6

Ans.
(4)

Slope of given lines are $m_{1} = \frac{1}{2}$ and $m_{2} = - 1$ .

Since, AB = AC, then $∠$ ABC = $∠$ ACB

Now, angle between AB and BC = angle between AC and BC

$\frac{m - \frac{1}{2}}{1 + \frac{1}{2} (m)} = \frac{- 1 - m}{1 - m}$

$\Rightarrow \frac{2 m - 1}{2 + m} = \frac{m + 1}{m - 1}$

$\Rightarrow 2 m^{2} - 3 m + 1 = m^{2} + 3 m + 2$

$\Rightarrow m^{2} - 6 m - 1 = 0$

Sum of roots = 6

$∴$ Required sum is 6.

Want Us to Email you About Special Offers & Updates?