Find the coordinates of point B on Line AC such that AB is 2/3 of AC (B is located in between A and C). A is (1,-5) and C is (-5,4).
C-A is (-6,9)
2/3 of that is (-4,6)
So, B = A + 2/3 (C-A) = (1,-5)+(-4,6) = (-3,1)
the coordinates of B are (2, -5)
To find the coordinates of point B on line AC such that AB is 2/3 of AC, we can use the concept of linear interpolation. Here's how you can do it:
1. Calculate the difference between the x-coordinates of points A and C: Δx = Cx - Ax = (-5) - 1 = -6.
2. Calculate the difference between the y-coordinates of points A and C: Δy = Cy - Ay = 4 - (-5) = 9.
3. Multiply the differences by 2/3 to find the corresponding change in x and y values: Δx' = (2/3) * Δx = (2/3) * (-6) = -4 and Δy' = (2/3) * Δy = (2/3) * 9 = 6.
4. Add the change in x and y values to the x-coordinate and y-coordinate of point A to find the coordinates of point B: Bx = Ax + Δx' = 1 + (-4) = -3 and By = Ay + Δy' = -5 + 6 = 1.
5. Therefore, the coordinates of point B on line AC such that AB is 2/3 of AC are (-3, 1).
Note: Linear interpolation calculates an intermediate point on a line segment by multiplying the change in x and y values by a fraction (in this case, 2/3) and adding the result to the starting coordinates.
A(1, -5), B(x, y), C(-5, 4).
x-1 = 2/3(-5-1).
x-1 = -4,
X = -3.
y-(-5) = 2/3(4-(-5)).
y+5 = 6,
Y = 1.