What are the coordinates of point B on AC such that AB=2/5AC
To find the coordinates of point B on line segment AC such that AB is equal to 2/5 times the length of AC, let's assume the coordinates of point C are (x1, y1) and the coordinates of point A are (x2, y2).
First, we need to find the length of AC. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the distance AC is equal to:
dAC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Next, we need to find the coordinates of point B, which would be the midpoint of AC. The midpoint formula states that the coordinates (x, y) of the midpoint between two points (x1, y1) and (x2, y2) are given by:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
In this case, the coordinates of point B would be:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Finally, we need to adjust the coordinates of point B such that AB is equal to 2/5 times the length of AC. We can use the proportion:
AB / AC = 2/5
To find the coordinates of point B, we can use the following formulas:
x = x1 + (2/5) * (x2 - x1)
y = y1 + (2/5) * (y2 - y1)
By substituting the known coordinates of point A and point C into these formulas, we can find the coordinates of point B.
well, first you gotta know the coordinates or the of A and C (or the length of AC).
So, divide the distance from A to C into 5ths, and add 2 of those to A.
That's where B is.