Question

If X(2, 3) and Y(a, 1) are 6 units apart, what is the value of a?

Show work please

Answer 1

`a=2+-4sqrt2`

Explanation:

.

You can use the distance formula:

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`6=sqrt((a-2)^2+(1-3)^2)=sqrt((a-2)^2+4`

`6^2=(a-2)^2+4`

`36=a^2-4a+4+4=a^2-4a+8`

`a^2-4a-28=0`

Using the quadratic formula:

`a=(4+-sqrt(16-4(1)(-28)))/(2(1))=(4+-sqrt128)/2=2+-(2sqrt32)/2`

`a=2+-sqrt32=2+-4sqrt2`