P and Q are points of trisection of a line segment joining points A(-8,12) and B (1,-3). P is nearer to A. Find the coordinates of P. Please answer ASAP!!
Ver bad
To find the coordinates of point P, we need to calculate the coordinates using the concept of trisection.
Step 1: Calculate the differences in x and y coordinates between points A and B.
Δx = Bx - Ax = 1 - (-8) = 9
Δy = By - Ay = -3 - 12 = -15
Step 2: Divide the differences by 3 to find the increments.
increment_x = Δx / 3 = 9 / 3 = 3
increment_y = Δy / 3 = -15 / 3 = -5
Step 3: Add the increments to the coordinates of point A to find the coordinates of point P.
Px = Ax + increment_x = -8 + 3 = -5
Py = Ay + increment_y = 12 + (-5) = 7
Therefore, the coordinates of point P are (-5, 7).
To find the coordinates of point P, we need to find the coordinates that are two-thirds of the way from point A to point B.
First, we find the differences in x-coordinates and y-coordinates between points A and B:
Δx = Bx - Ax = 1 - (-8) = 9
Δy = By - Ay = -3 - 12 = -15
Next, we determine the increment for each coordinate by dividing Δx and Δy by 3:
Increment_x = Δx / 3 = 9 / 3 = 3
Increment_y = Δy / 3 = -15 / 3 = -5
Starting from point A, we apply the increments to find point P:
Px = Ax + Increment_x = -8 + 3 = -5
Py = Ay + Increment_y = 12 - 5 = 7
Therefore, the coordinates of point P are (-5, 7).
P is 1/3 of the way from A to B.
The difference in coordinates when moving from A to B is (9,-15)
So, P = A+(3,-5) = (-8,12)+(3,-5) = (-5,7)
and Q = (-5,9) + (3,-5) = (-2,4)
Finally, adding another (3,-5) gets you to (1,-3) = B
If P is 1/n of the way from A to B, P = A + 1/n (B-A)