Question

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.

Answer 1

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, ...

Answer 2

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).