The length of the line segment joining A(2,-1) and B(5,y) is 5 units. What is y?

1 Answer
Jim G.
Jan 24, 2018

#y=-5" or "y=3#

Explanation:

#"use 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,-1)" and "(x_2,y_2)=(5,y)#

#d=sqrt((5-2)^2+(y+1)^2)=5#

#rArrd=sqrt(9+(y+1)^2)=5#

#color(blue)"squaring both sides"#

#rArr9+(y+1)^2=25#

#rArr(y+1)^2=25-9=16#

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

#rArry+1=+-sqrt16larrcolor(blue)"note plus or minus"#

#rArry+1=+-4#

#rArry=-1+-4#

#rArry=-1-4" or "y=-1+4#

#rArry=-5" or "y=3#

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