Answer:
D(3.4, 20.8)
Explanation:
Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.
Slope
The equation for the slope between two points is ...
m = (y2 -y1)/(x2 -x1)
Using this formula and the given points, we can find D(x, y) to satisfy ...
2 = (y -10)/(x +2)
-3 = (y -7)/(x -8)
Solution
Putting each of these equations in general form, we have ...
2(x +2) -(y -10) = 0
2x -y +14 = 0
and
-3(x -8) -(y -7) = 0
3x +y -31 = 0
Adding the two equations eliminates the y-variable:
(2x -y +14) +(3x +y -31) = 0
5x -17 = 0 . . . . . . simplify
x -3.4 = 0 . . . . . . divide by 5
x = 3.4 . . . . . . . . . add 3.4
Substituting for x in the first equation gives ...
2(3.4) -y +14 = 0
y = 6.8 +14 = 20.8 . . . . add y
The point D has coordinates (3.4, 20.8).
__
Additional comment
The graph shows the equations of the lines written in point-slope form.