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Question: The point on y-axis equidistant from the points (3, 2) and (–1, 3) is ....

The point on 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)

Answer

(0, –3/2)

Explanation

Solution

Point on y-axis is (0, b), therefore by given condition (0−3)2+(b−2)2=(0+1)2+(b−3)2( 0 - 3 ) ^ { 2 } + ( b - 2 ) ^ { 2 } = ( 0 + 1 ) ^ { 2 } + ( b - 3 ) ^ { 2 }

⇒9+b2+4−4b=1+b2+9−6b⇒b=−32\Rightarrow 9 + b ^ { 2 } + 4 - 4 b = 1 + b ^ { 2 } + 9 - 6 b \Rightarrow b = - \frac { 3 } { 2 }

Hence the point is (0,−32)\left( 0 , - \frac { 3 } { 2 } \right).