K(-3, 2) and L(3, m) are 9 units apart. What is the value of m?

Show work and explain please

1 Answer
Jim G.
Dec 5, 2017

#m=2+-3sqrt5#

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)|)))#

#"this calculates the distance d between 2 points"#

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

#d=sqrt((3-(-3))^2+(m-2)^2)=9larrcolor(blue)"9 units apart"#

#color(blue)"square both sides"#

#(sqrt((36+(m-2)^2)))^2=9^2#

#rArr36+(m-2)^2=81#

#"subtract 36 from both sides"#

#cancel(36)cancel(-36)+(m-2)^2=81-36#

#rArr(m-2)^2=45#

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

#sqrt((m-2)^2)=+-sqrt45larrcolor(blue)"note plus or minus"#

#rArrm-2=+-sqrt(9xx5)=+-3sqrt5#

#"add 2 to both sides"#

#mcancel(-2)cancel(+2)=2+-3sqrt5#

#rArrm=2+-3sqrt5larrcolor(blue)"exact values"#

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