Help solving? What are the possible values of x and y? Line AB is perpendicular to Line CD. A(1,3). B(4, -2). C(6,1). D(x, y). Answer choices...

Since AB is perpendicular to
AC

Then the product of the slopes =
-1

Let m1 be the slope for
AB:

==> m1= (-2-3)/(4-1) =
-5/3

Let m2 be the slope for
CD

==> m1*m2 =
-1

==> -5/3 *m2 =
-1

==: m2 = 3/5

but m2 =
(y-1)/(x-6) = 3/5

==> y-1 =
(3/5)(x-6)

==> y= (3/5)(x-6) +
1

=> y= (3/5)x - 18/5 +
5/5

==> y= (3/5)x -
13/5

Therfore , we need x, y alues that verifies the
equation,

Let us substitute the
choices:

A( 1, -2)

==>
y= (3/5)*1 - 13/5

           = 3/5 - 13/5 = -10/5 =
-2

The point (1, -2) verifies the
equation.

Then D = (1,
-2)