Question

What is the coordinate of point P that lies along the directed line segment from Q(2, 5) to R(7, 12) and partitions the segment in the ratio of 3 to 2? (3, 4.2) (4.5, 8.5) (5, 9.2) (5, 7)

Answer 1

Answer:

(C)(5,9.2)

Step-by-step explanation:

Given points Q(2, 5) and R(7, 12). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 3 to 2.

For internal division of a line segment, the coordinate of the point which partitions the segment in the ratio m:n is given as:

$\left(\dfrac{mx_2+nx_1}{m+n} , \dfrac{my_2+ny_1}{m+n}\right)$

m:n =3:2

$(x_1,y_1)=Q(2,5)\\(x_2,y_2)=R(7,12)$

Therefore:

$P(x,y)=\left(\dfrac{3*7+2*2}{3+2} , \dfrac{3*12+2*5}{3+2}\right)\\=\left(\dfrac{25}{5} , \dfrac{46}{5}\right)\\P(x,y)=(5,9.2)$