The length of the line segment joining A(2,8) and B(12,y) is 26 units. What is y?

2 Answers
Jan 27, 2018

#color(red)(y = 32 or -16)# units

Explanation:

Distance between two points is calculated using the formula,

#d = sqrt((x2-x1)^2 + (y2 - y1)^2)#

Given : x1 = 2, x2 = 12, y1 = 8, y2 = y & d = 26 units

#:. 26 = sqrt((12-2)^2 + (y - 8)^2)#

Squaring both sides,

#10^2 + (y-8)^2 = 26^2#

#(y-8)^2 = 26^2 - 10^2 = 576 = 24^2#

Taking square root on both sides,

#y-8 = +-24#

#color(red)(y) = 24 + 8 = color(red)(32)# units or

#color(red)(y) = -24 + 8 = color(red)(-16)# units

Jan 27, 2018

#y=-16" or "y=32#

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)=(2,8)" and "(x_2,y_2)=(12,y)#

#d=sqrt((12-2)^2+(y-8)^2)=26#

#rArrd=sqrt(100+(y-8)^2)=26#

#color(blue)"square both sides"#

#rArr100+(y-8)^2=26^2=676#

#rArr(y-8)^2=676-100=576#

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

#rArry-8=+-24larrcolor(blue)"note plus or minus"#

#rArry=8+-24#

#rArry=8-24=-16" or "y=8+24=32#