MATH SOLVE

4 months ago

Q:
# 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)

Accepted Solution

A:

Answer:Point N(3,0) is equidistant from A and B.Step-by-step 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 JAJ= √((-4-0)^2+(-5+4)^2 )=√((-4)^2+(-1)^2 )= √(16+1)= √17 unitsBJ=√((-4+2)^2+(-5-0)^2 )=√((-2)^2+(-5)^2 )= √(4+25)= √29 unitsPoint J is not equidistant from A and B.For KAK= √((-3-0)^2+(0+4)^2 )=√((-3)^2+(4)^2 )= √(9+16)= √25 units=5BK=√((-3+2)^2+(0-0)^2 )=√((-1)^2+(0)^2 )= √(1+0)= √1 =1 unitPoint K is not equidistant from A and B.For MAM= √((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 unitsPoint M is not equidistant from A and B.For NAN= √((3-0)^2+(0+4)^2 )=√((3)^2+(4)^2 )= √(9+16)= √25=5 unitsBN=√((3+2)^2+(0-0)^2 )=√((5)^2+(0)^2 )= √(25+0)= √25 =5 unitsAs point N's distance is equal from A and B, Point N is equidistant from A and B..