Solve this problem (coordinate geometry)?
Topic: Explain the problem solving method
May 22, 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).
👍 218 | 👎 5
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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.
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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graph those factors and traces -draw xOy coordinate gadget -use color pencil draw line x=0[ it rather is actual the y-axis] draw the line for 3y=x or y=x/3 - hit upon element A and C -from A draw a line passing by way of A. parallel to the y axis[ line x=0] do a similar for element C -from A draw a line parallel to line y=x/3 do a similar for C - final step discover the gap from A to B on account that AC//line y=x/3, they could desire to have a similar slope. use element-slope (y-y1) = m (x - x1) to place in writing the equation for line AC, do a similar for line CD on account that B is on a similar line with C, it may desire to have a similar x -value[x=4) x=4, you in user-friendly terms ought to discover y factors A and D could desire to have a similar x value[ x= -2]
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BC has a Slop of 1
AD must have a slop of -1
line BC has the equation y = x+2
Ad has the equation y=-x+6
they intercept in (2/4)
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