Question

Point j(-2,1) and point K(4,5) form line segment JK. For the point P that partitions JK in the ratio 3:7, what is the y- coordinate of P?

Answer 1

2.2

Explanation:

We have been given that point J(-2,1) and point K(4,5) form line segment JK. The point P partitions JK in the ratio 3:7.

To find the y-coordinate of point P we will use section formula, when a point A divides a segment JK internally in the ratio m:n.

`[x=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)]`

Upon substituting our given values in above formula we will get,

`[x=(3*4+7*-2)/(3+7),y=(3*5+7*1)/(3+7)]`

`[x=(12-14)/(10),y=(15+7)/(10)]`

`[x=(-2)/(10),y=(22)/(10)]`

`[x=-0.2,y=2.2]`

Therefore, the y-coordinate of point P is 2.2.

Answer 2

If
`J(x_1,y_1)` and
`K(x_2,y_2)` are two points, then
`P((nx_1+mx_2)/(m+n),(ny_1+my_2)/(m+n))` partitions JK in the ratio,
`m:n`.

The y-coordinate of P is

`y=(ny_1+my_2)/(m+n)=(7*1+3*5)/(3+7)=(11)/(5)`