Determine the values of y when the distance between #(-7,y)# and #(-3,4)# is #4 sqrt5#?

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Answer 1 · 2018-05-18T10:38:28

#y_1=-4# and #y_2=12#

After using formula distance between 2 points,

#sqrt(((-3)-(-7))^2+(4-y)^2)=4sqrt5#

#sqrt(4^2+(4-y)^2)=4sqrt5#

#sqrt(y^2-8y+32)=4sqrt5#

#y^2-8y+32=(4sqrt5)^2#

#y^2-8y+32=80#

#y^2-8y-48=0#

#(y+4)*(y-12)=0#

Thus #y_1=-4# and #y_2=12#