Respuesta :
Answer:
A and B
Step-by-step explanation:
If point P (x,y) lies on line segment [tex]\overline{AB}[/tex] (between points A and B) and satisfies AP:PB=m:n, then we say that P divides [tex]\overline{AB}[/tex] internally in the ratio m:n. The point of division has the coordinates
[tex]P=\left( \dfrac{mx_2 + nx_1}{m+n}, \dfrac{my_2 + ny_1}{m+n} \right).[/tex]
CORRECT
- Line segment AB has endpoints A(5, 4) and B(2,7). The coordinates (4,5) divides the line segment directed from A to B in the ratio of 1:2
[tex]P=\left( \dfrac{1*2 + 2*5}{2+1}, \dfrac{1*7 + 2*4}{2+1} \right)=(4,5)[/tex]
- Line segment AB has endpoints A(6,5) and B(3,8). The coordinates (5,6) divides the line segment directed from A to B in the ratio of 1:2.
[tex]P=\left( \dfrac{1*3 + 2*6}{2+1}, \dfrac{1*8 + 2*5}{2+1} \right)=(5,6)[/tex]
INCORRECT
- Line segment AB has endpoints A(5,7) and B(8,4). The coordinates (6,5) divides the line segment directed from A to B in the ratio of 1:2.
[tex]P=\left( \dfrac{1*8 + 2*5}{2+1}, \dfrac{1*4 + 2*7}{2+1} \right)=(5,6)[/tex]
- Line segment AB has endpoints A(7, 2) and B(4,8). The coordinates (5, 4) divides the line segment directed from A to B in the ratio of 1:2.
[tex]P=\left( \dfrac{1*4 + 2*7}{2+1}, \dfrac{1*8 + 2*2}{2+1} \right)=(6,4)[/tex]
REMARK
A and B are correct. However the coordinates of P for C and D are incorrect.
