Find the equation of the line from B(-8, -3) to C(4, 6). I am assuming that point A is at the origin. You can do this by finding the slope of the line, and then the point-slope form of the equation of a line.MathMan2022 said:But don't know howto proceed from there?
Although it may not the required/intended method, note that the problem can easily be done with only simple geometry and proportionality.MathMan2022 said:Homework Statement:: Lets image we have two vectors AC = <4,6> and AB = <-8,-3> then find a point D which lies on the vector BC which satisfies that |BD|/|CD| = 5/6 ??
Relevant Equations:: |BD| = 5/6 |CD|
Not sure on howto proceed here?
To find the coordinates of point D on the vector BC, you need to know the coordinates of points B and C. If D divides the vector BC in the ratio m:n, you can use the section formula: D = [(m*C_x + n*B_x)/(m+n), (m*C_y + n*B_y)/(m+n)], where B(x1, y1) and C(x2, y2).
The section formula is a mathematical formula used to find the coordinates of a point that divides a line segment joining two given points in a specified ratio. For a point D dividing the line segment BC in the ratio m:n, the coordinates are given by: D = [(m*C_x + n*B_x)/(m+n), (m*C_y + n*B_y)/(m+n)].
If point D is the midpoint of vector BC, the ratio m:n is 1:1. Therefore, the coordinates of D can be found using the midpoint formula: D = [(B_x + C_x)/2, (B_y + C_y)/2].
If point D lies outside the segment BC, you can still use the section formula, but the ratio m:n will be negative. For example, if D divides BC externally in the ratio m:n, the coordinates are given by: D = [(m*C_x - n*B_x)/(m-n), (m*C_y - n*B_y)/(m-n)].
Sure! Let's say B has coordinates (2, 3) and C has coordinates (8, 7), and D divides BC in the ratio 2:3. Using the section formula:D = [(2*8 + 3*2)/(2+3), (2*7 + 3*3)/(2+3)] = [(16 + 6)/5, (14 + 9)/5] = [22/5, 23/5] = (4.4, 4.6).