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)y=32or16 units

Explanation:

Distance between two points is calculated using the formula,

d = sqrt((x2-x1)^2 + (y2 - y1)^2)d=(x2x1)2+(y2y1)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