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? Your answer: (3, 4.2) (4.5, 8.5) (5, 9.2) (5, 7)

Answer 1

Answer:

Option (3). (5, 9.2)

Step-by-step explanation:

If Point P divides the line segment QR in the ratio of m : n.

Let the coordinates of the point P are (x, y)

Since coordinates of the point P are given by,

x = $\frac{m(x_2)+n(x_1)}{m+n}$

y = $\frac{m(y_2)+n(y_1)}{m+n}$

Where $(x_1, y_1)$ and $(x_2,y_2)$ are the ordered pairs representing points Q and R.

If $(x_1,y_1)$ represents (2, 5) and $(x_2,y_2)$ represents (7, 12),

Coordinates of point P(x, y) which divides the segment in the ratio of 3:2.

x = $\frac{3(7)+2(2)}{3+2}$

x = $\frac{25}{5}=5$

y = $\frac{3(12)+2(5)}{3+2}$

y = $\frac{46}{5}=9.2$

Therefore, Point P will be represented by (5, 9.2)

Option (3) will be the answer.