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

2 Answers
May 18, 2018

x=0 or -2

Explanation:

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

May 18, 2018

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

Explanation:

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