Question

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

Answer 1

`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

Answer 2

`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`