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

Option (3). (5, 9.2)

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 =
`(m(x_2)+n(x_1))/(m+n)`

y =
`(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 =
`(3(7)+2(2))/(3+2)`

x =
`(25)/(5)=5`

y =
`(3(12)+2(5))/(3+2)`

y =
`(46)/(5)=9.2`

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

Option (3) will be the answer.