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# Solve this problem (coordinate geometry)?

Topic: Explain the problem solving method
July 18, 2019 / By Adrea
Question: A(0,6) B(1,3) and C(4,6) are three points. D is the foot of the perpendicular from A to BC. Find the coordinates of D? help and explain your method thoroughly please?

## Best Answers: Solve this problem (coordinate geometry)?

Terance | 5 days ago
You get the equation of line BC by using the two-point form and the line AD by using the point-slope form (you have point A, the negative reciprocal of the slope of line BC as your slope for line AD). The equations are: line BC x - y = - 2 line AD x + y = 6 If you solve these 2 equations simultaneously, you get their point of intersection which is (2, -4).
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We found more questions related to the topic: Explain the problem solving method

Originally Answered: Coordinate Algebra and Geometry?
1) slope of the line ∙ ∙ change in y, 1 → -8, is -9 ∙ ∙ change in x, 2 → -1, is -3 ∙ ∙ ∙ so slope is -9/-3 = 3 ∙ ∙ using (2,1) as the point (x1, y1) the equation is ∙ ∙ y – 1 = 3(x – 2) ∙ ∙ that's point-slope form. 2) if you have the slope you don't need a 2nd point to find it, just fill in the form as above. 3) pick an x, compute the y. intercepts are easy since one of your picks is 0. ∙ ∙ so for 2x + y = 9, when ∙ ∙ x = 0, y = 9 ∙ ∙ ∙ and when ∙ ∙ x = 1, y = 7 notice slope is -2, so when x goes up 1, y goes down 2. should make plotting points easy.

Pierce
Equation of line passing to B and C is y - 3 = (6-3)/(4-1)(x-1) or y = x +2 Slope of perpendicular to this line is - 1 and must passes to A(0,6) then equation of line passes to A and D is y -6 = -1(x-0) then y = -x+6 Intersection of y = x+2 and y = -x+6 is point D x = 2 and y = 4 D(2 , 4)
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