The coordinates of A and B are (7,-7) and (-2,2) respectively. If P and Q divide the line segment AB into 3 equal parts, find the coordinates of P and Q.
Both x and y change by 9, so move along 1/3 of the way for P and Q.
I'll do P, and you should have to trouble finding Q.
x changes by -9 going from A to B, and y changes by +9. So, add (-3,3) to (7,-7) to get (4,-4).
Or, more formally,
Px = Ax + 1/3 (Bx - Ax)
Py - Ay + 1/3 (By - Ay)
for Q, ...
A(7,-7),P(x1,y1),Q(x2,y2),B(-2,2).
AP = AB/3,
x1-7 = (-2-7)/3,
x1-7 = -3,
X1 = 4.
y1-(-7) = 2-(-7)/3,
y1+7 = 3,
Y1 = -4.
AQ = (2/3)AB.
x2-7 = (2/3)(-2-7),
x2-7 = -6,
X2 = 1.
y2-(-7) = (2/3)(2-(-7),
y2+7 = 6,
Y2 = -1.
A(7,-7),P(4,-4),Q(1,-1),B(-2,2).
To find the coordinates of point P and Q, we will divide the line segment AB into three equal parts.
Step 1: Find the difference in x-coordinates and y-coordinates
The difference in x-coordinates (Δx) = x2 - x1 = -2 - 7 = -9
The difference in y-coordinates (Δy) = y2 - y1 = 2 - (-7) = 9
Step 2: Divide the difference by 3
Divide both Δx and Δy by 3 to find the increment for each part:
Δx/3 = -9/3 = -3
Δy/3 = 9/3 = 3
Step 3: Compute the coordinates of P and Q
Starting from point A(7,-7), we will move -3 in the x-direction for P and -6 in the x-direction for Q (since we need to divide into three equal parts).
For point P:
x-coordinate of P = x-coordinate of A + (-3) = 7 + (-3) = 4
y-coordinate of P = y-coordinate of A + 3 = -7 + 3 = -4
Therefore, the coordinates of P are (4, -4).
For point Q:
x-coordinate of Q = x-coordinate of A + (-6) = 7 + (-6) = 1
y-coordinate of Q = y-coordinate of A + 6 = -7 + 6 = -1
Therefore, the coordinates of Q are (1, -1).
So, the coordinates of P and Q are (4,-4) and (1,-1) respectively.