Determine the value of x when (-1,-1)is equidistant from (0,2)and(x,-4)?

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Answer 1 · 2018-05-18T12:11:02

#x=0 or -2#

Using distance formula / Pythagorean theorem,

Let the distance between #(-1,-1)# and #(0,2)# be #d_1#,

#d_1=sqrt((-1-0)^2+(-1-2)^2)#
#color(white)(d_1)=sqrt10#

Let the distance between #(-1,-1)# and #(x,-4)# be #d_2#,

#d_2=sqrt((-1-x)^2+(-1+4)^2)#
#color(white)(d_2)=sqrt((-1-x)^2+9)#

Since, the distance are the same, #d_1=d_2#

#sqrt10=sqrt((-1-x)^2+9)#

Square both sides,

#10=(-1-x)^2+9#

Subtract #9# from both sides,

#(-1-x)^2=1#

Square root both sides,

#-1-x=+-1#

Solve,

#x=0 or -2#

Answer 2 · 2018-05-18T12:14:39

#color(crimson)(x = 0 # or #color(crimson)(-2#

Given #A(-1,-1), B(0,2), C(x,-4), bar(AB) = bar(AC)# To find x

Distance formula #d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)#

#bar(AB) = sqrt((-1-0)^2 + (-1-2)^2) = sqrt10#

#bar(AC) = sqrt((-1-x)^2 + (_1+4)^2) #

Bus #bar(AB) = bar(AC)#

#sqrt((-1-x)^2 + 3^2) = sqrt 10#

Squaring both sides,

#(x+1)^2 + 9 = 10#

#(x+1)^2 = 1 = 1^2#

#x+1 = +-1#

#color(crimson)(x = 0, -2#