Question

AB ¯ ¯ ¯ ¯ ¯ ¯ has endpoints A(2, 4) and B(8, y). If AB is 10, what is the value of y?

Answer 1

Answer: The value of y is 12 or -4 .

Step-by-step explanation:

It is given that the two endpoints of AB are A(2,4) and B(8,y). The length of AB is 10.

Distance formula is,

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`AB=√((8-2)^2+(y-4)^2)`

`10=√((6)^2+y^2-8y+16)`

Squaring both sides.

`100=36+y^2-8y+16`

`y^2-8y+52-100=0`

`y^2-8y-48=0`

Use grouping method to find the factors.

`y^2-12y+4y-48=0`

`y(y-12)+4(y-12)=0`

`(y-12)(y+4)=0`

Equate each factor equal to 0.

`y-12=0`

`y=12`

`y+4=0`

`y=-4`

Therefore the values of y are either 12 or -4.