Question

Line segment AB has endpoints A(−5,−8) and B(2,6). What are the coordinates of the point that partitions AB according to the part-to-part ratio 4:3?
O (-1, 0)
O (-2, -2)
O (-4, -6)
O (0, -1)

Line segment BA has endpoints B(−6,1) and A(4,6).
What are the coordinates of the point that partitions BA
according to the part-to-part ratio 2:3?
O (4, 0)
O (-2, 3)
O (3, -2)
O (0, 4)

Line segment AB has endpoints A(−1,6) and B(5,−6).
What are the coordinates of the point that partitions AB
according to the part-to-part ratio 1:5?
O (4, 0)
O (0, 4)
O (-4, 4)
O (4, -4)

Answer 1

For all 3 questions, we will use the section formula.

1) $\left(\frac{(4)(2)+(3)(-5)}{7}, \frac{(4)(6)+(3)(-8)}{7} \right)=\boxed{(-1, 0)}$

2) $\left(\frac{(2)(4)+(3)(-6)}{5}, \frac{(2)(6)+(3)(1)}{5} \right)=\boxed{(-2, 3)}$

3) $\left(\frac{(1)(5)+(5)(-1)}{6}, \frac{(1)(-6)+(5)(6)}{6} \right)=\boxed{(0, 4)}$