If X(-2, 3) and Y(a, -1) are 6 units apart, what is the value of a?

Show work and explain please

1 Answer
Jim G.
Dec 4, 2017

#a=-2+-2sqrt5#

Explanation:

#"using the "color(blue)"distance formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)color(white)(2/2)|)))#

#"let "(x_1,y_1)=(-2,3)" and "(x_2,y_2)=(a,-1)#

#rArrd=sqrt((a+2)^2+(-1-3)^2)=6#

#color(blue)"square both sides"#

#(a+2)^2+16=36#

#rArr(a+2)^2=36-16=20#

#color(blue)"take the square root of both sides"#

#sqrt((a+2)^2)=+-sqrt20larrcolor(blue)"note plus or minus"#

#rArra+2=+-2sqrt5#

#rArra=-2+-2sqrt5#

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