Question

Given the points B(-2, 10) and C(8, 7), find one point D that makes both statements true.

The slope of the line connecting B and D is 2. The slope of the line connecting C and D is - 3.

Answer 1

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).

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Additional comment

The graph shows the equations of the lines written in point-slope form.