Question

Which of the following points is an equal distance (equidistant) from A(0, −4) and B(−2, 0)?

J(−4, −5)
K(−3, 0)
M(0, 0)
N(3, 0)

Answer 1

Point N(3,0) is equidistant from A and B.

Explanation:

In order to check whether the point is equidistant from A and B, it is required to measure the distance of A and B from each point. The formula for distance is:

d= √((x_2-x_(1))^2+(y_2-y_(1))^2 )

For J

AJ= √((-4-0)^2+(-5+4)^2 )

=√((-4)^2+(-1)^2 )

= √(16+1)

= √17 units

BJ=√((-4+2)^2+(-5-0)^2 )

=√((-2)^2+(-5)^2 )

= √(4+25)

= √29 units

Point J is not equidistant from A and B.

For K

AK= √((-3-0)^2+(0+4)^2 )

=√((-3)^2+(4)^2 )

= √(9+16)

= √25 units

=5

BK=√((-3+2)^2+(0-0)^2 )

=√((-1)^2+(0)^2 )

= √(1+0)

= √1

=1 unit

Point K is not equidistant from A and B.

For M

AM= √((0-0)^2+(0+4)^2 )

=√((0)^2+(4)^2 )

= √(0+16)

= √16

=4 units

BM=√((0+2)^2+(0-0)^2 )

=√((2)^2+(0)^2 )

= √(4+0)

= √4

=2 units

Point M is not equidistant from A and B.

For N

AN= √((3-0)^2+(0+4)^2 )

=√((3)^2+(4)^2 )

= √(9+16)

= √25

=5 units

BN=√((3+2)^2+(0-0)^2 )

=√((5)^2+(0)^2 )

= √(25+0)

= √25

=5 units

As point N's distance is equal from A and B, Point N is equidistant from A and B.

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