Finding the Coordinates of Point D

In summary, we have points A(1,3), B(5,1), and C(2,-8) with coordinates. Point D has coordinates (m,n) and is located at the intersection of the vectors AD = Vector BC + (2x) vector AB + (3y) vector AC = vector AB + (2x) vectorAC + (3y) vector BC. By solving the system of equations, we can determine the coordinates of D, which are (m,n) = (3,-7).
  • #1
Ecdownes
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Points A ,B and C have coordinates A(1,3) B(5,1) and C(2,-8).
point D is such that the vector AD = Vector BC + (2x) vector AB + (3y) vectorAC = vector AB + (2x) vectorAC + (3y) vector BC
find coordinates of D
 
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  • #2
AB = (4,-2), BC = (-3,-9), AC = (1,-11)

let D = (m,n) $\implies$ AD = (m-1,n-3)

AD = (-3,-9) + 2x(4,-2) + 3y(1,-11) = (4,-2) + 2x(1,-11) + 3y(-3,-9)

AD = (-3+8x+3y , -9-4x-33y) = (4+2x-9y , -2-22x-27y)

-3+8x+3y = 4+2x-9y
-9-4x-33y = -2-22x-27y

solve the system for x and y, then determine the coordinates of D
 

1. How do I find the coordinates of Point D on a graph?

To find the coordinates of Point D, you will need to know the x and y values of the point. These values represent the horizontal and vertical position of the point on the graph. You can find these values by looking at the intersection of the point with the x-axis and y-axis, respectively.

2. What is the importance of finding the coordinates of Point D?

The coordinates of Point D are important because they provide specific information about the location of the point on the graph. This information can be used to calculate distances, determine slopes, and solve equations involving the point.

3. Can I use any method to find the coordinates of Point D?

Yes, there are multiple methods that can be used to find the coordinates of Point D. The most common methods include using the distance formula, solving equations, and using the slope-intercept form of a line.

4. Is it possible to find the coordinates of Point D if I only know the coordinates of other points on the graph?

Yes, it is possible to find the coordinates of Point D if you know the coordinates of other points on the graph. You can use the distance formula or solve equations to determine the coordinates of Point D based on the known points.

5. Can I find the coordinates of Point D without using a graph?

Yes, it is possible to find the coordinates of Point D without using a graph. This can be done by solving equations or using the distance formula, as long as you have enough information about the point's location or its relationship to other points on the graph.

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