Which point is on the line that passes through point R and is perpendicular to line PQ? (–6, 10) (–4, –8) (0, –1) (2, 4)

(-4, -8)

Step-by-step explanation:

Let the coordinates of common point of the given lines are (x, y),

Thus, the slope of the line passes through the points (a, b) and R(4,2) is,

       2 - b

m1 = ------

        4 - a

Again, the slope of the line passes through two points P(-6,4) and Q(4,-4),

      -4 - 4          -8           -8          -4

m2 = ------  =   --------- = --------- = ---------

        4- (-6)       4 + 6         10        5

= m1 * m2 = -1

  2 - b      -4

= -------   x ---- =  -1

   4 - a      5

        8 - 4b

=     -----------   = 1

        20 - 5a

= 8 - 4b  = 20 - 5a

= 5a - 4b = 12 --------- equation 1

For a = -6   and b = -10

5 x -6  - 4  x  10 = -70 ≠ 12

For a = -4   and b = -8

5 x -4  - 4  x  - 8  = 12 = 12

For a = 0  and b = -1

5 x 0 - 4 x -1 = 4 ≠ 12

For a = 2 and b = 4

5 x 2 - 4 x 4 = -6 ≠ 12

therefore Second is correct

hope it helps and i get the brainliest.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.