please help im really struggling
Point A is located at (2, 6) and point B is located at (18, 12).
What point partitions the directed line segment AB¯¯¯¯¯ into a 2:3 ratio?
i know that this deals with the midpoint formula and stuff like that
THANK YOU !
let the point be P(x,y)
you don't say if AP : PB = 2 : 3 or 3 : 2
I will assume the first. If otherwise it is very easy to change
If you make a sketch and draw the right-angled triangles, you can see ....
for the x:
(x-2)/(18-x) = 2/3
3x - 6 = 36 - 2x
5x = 42
x = 8.4
find y in the same way
Point A has coordinates A(1, 4) and point B has coordinates B(5, 1). Find the coordinates of the midpoint M of AB?
c3rfr3f3f34f4f3 is the odds of 6 so do whatevr
I'm here to help! To find the point that partitions the directed line segment AB into a 2:3 ratio, we need to use the concept of a "section formula" or "internally dividing a line segment."
The section formula states that if a line segment AB is divided by a point P in the ratio m:n (where m and n are non-zero integers), then the coordinates of point P can be found using the following formula:
Px = (n * Ax + m * Bx) / (m + n)
Py = (n * Ay + m * By) / (m + n)
Now, let's plug in the given values for points A and B:
Ax = 2, Ay = 6 (coordinates of point A)
Bx = 18, By = 12 (coordinates of point B)
m = 2 (ratio benefit)
n = 3 (ratio benefit)
Using the section formula, we can calculate the coordinates of point P:
Px = (3 * 2 + 2 * 18) / (2 + 3)
Py = (3 * 6 + 2 * 12) / (2 + 3)
Simplifying the equations, we have:
Px = (6 + 36) / 5
Py = (18 + 24) / 5
Therefore, the coordinates of the point that partitions the line segment AB into a 2:3 ratio are:
P = (8.4, 12)
The point P is located at (8.4, 12)
the x distance is ... 18 - 2 = 16
2/5 * 16 = 32/5 = 6.4
Ax + 6.4 = 8.4
the y distance is ... 12 - 6 = 6
2/5 * 6 = 12/5 = 2.4
Ay + 2.4 = 8.4
partition point ... (8.4,8.4)