(B) Let the point on the $y$-axis be $P(0, y)$.Since $P$ is equidistant from $A(3, 2)$ and $B(-1, 3)$,we have $PA^2 = PB^2$.$(0 - 3)^2 + (y - 2)^2 = (

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Let the point on the $y$-axis be $P(0, y)$.Since $P$ is equidistant from $A(3, 2)$ and $B(-1, 3)$,we have $PA^2 = PB^2$.$(0 - 3)^2 + (y - 2)^2 = (0 - (-1))^2 + (y - 3)^2$$9 + y^2 - 4y + 4 = 1 + y^2 - 6y + 9$$13 - 4y = 10 - 6y$$2y = -3$$y = -\frac{3}{2}$Therefore,the required point is $(0, -\frac{3}{2})$.

Class 11 Mathematics Straight Lines System of co-ordinates, Distance between two points, Section formulae

Easy

The point on the $y$-axis equidistant from the points $(3, 2)$ and $(-1, 3)$ is

A
$(0, -3)$
B
$(0, -3/2)$
C
$(0, 3/2)$
D
$(0, 3)$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Lines

Subtopic

System of co-ordinates, Distance between two points, Section formulae

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

Difficult

View Solution

The point which divides externally the line joining the points $(a + b, a - b)$ and $(a - b, a + b)$ in the ratio $a:b$ is

Easy

View Solution

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

Medium

View Solution

Find the points of trisection of the line segment joining the points $A(2, 1)$ and $B(5, 3)$.

Medium

View Solution

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The point on the $y$-axis equidistant from the points $(3, 2)$ and $(-1, 3)$ is

Similar Questions

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

The point which divides externally the line joining the points $(a + b, a - b)$ and $(a - b, a + b)$ in the ratio $a:b$ is

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

Find the points of trisection of the line segment joining the points $A(2, 1)$ and $B(5, 3)$.

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module