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 .

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,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB=\sqrt{(8-2)^2+(y-4)^2}$

$10=\sqrt{(6)^2+y^2-8y+16}$

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.