In a $\Delta ABC$, suppose $y=x$ is the equation of the bisector of the angle $B$ and the equation of the side $AC$ is $2x-y=2$. If $2AB=BC$ and the points $A$ and $B$ are respectively $(4,6)$ and $(\alpha,\beta)$, then $\alpha+2\beta$ is equal to

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

In a

\Delta ABC

, suppose

y=x

is the equation of the bisector of the angle

B

and the equation of the side

AC

2x-y=2

. If

2AB=BC

and the points

A

and

B

are respectively

(4,6)

and

(\alpha,\beta)

, then

\alpha+2\beta

is equal to

(1) $39$
(2) $42$ Official answer
(3) $45$
(4) $48$

Official answer

Option 2

NTA final key.

Chapter: Straight Lines
Topic: Straight Line Distance
Idea tested: Image of a point in a line

Same idea in other shifts

Asked 3× in all

9 Apr 2024, Shift 1 · Q14A ray of light coming from the point $P(1,2)$ gets reflected from the point Q on the $x$ -axis and then passes through the point $R(4,3)$ .…MediumSingle correct
6 Sep 2020, Shift 2 · Q64Let L denote the line in the $xy$ -plane with $x$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.