Question

Find x so the distance between (x, 2) and (2, 4) is the square root of 13. How do you work this?

Answer 1

`d= √((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ √(13) = √((2-x_1)^2+(4-2)^2) \\ \\ √(13) = √((2-x_1)^2+(2)^2) \\ \\ √(13) = √((2-x_1)^2+4) \\ \\ √(13) = √((2-x_1)*(2-x_1)+4) \\ \\ √(13) = √(4-2x_1-2x_1+(x_1)^2+4) \\ \\ (√(13))^2 = (√(-4x_1+(x_1)^2+8))^2 \\ \\ 13=(x_1)^2-4x_1+8 \\ \\ (x_1)^2-4x_1-5=0 \\ \\ (x_1-5)(x_1+1)=0 \\ \\ x_1=5,x_1=-1`

x can either equal 5 or -1