Three points 2

The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.

Correct answer:

x =  6.2
y =  9.6

Step-by-step explanation:


(x-3)·(6-3) + (y-8)·(2-8) = 0
(x-10) = (y-2) · (6-3)/(2-8)

3x-6y = -39
x+0.5y = 11

Row 2 - 1/3 · Row 1 → Row 2
3x-6y = -39
2.5y = 24


y = 24/2.5 = 9.6
x = -39+6y/3 = -39+6 · 9.6/3 = 6.2

x = 31/5 = 6.2
y = 48/5 = 9.6

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