The length of the line segment joining A(2,-1) and B(5,y) is 5 units. What is y?
1 Answer
Jan 24, 2018
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#