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

Answer:

2.2

Step-by-step 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.      

$[x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}]$  

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

$[x=\frac{3*4+7*-2}{3+7},y=\frac{3*5+7*1}{3+7}]$

$[x=\frac{12-14}{10},y=\frac{15+7}{10}]$

$[x=\frac{-2}{10},y=\frac{22}{10}]$

$[x=-0.2,y=2.2]$  

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 $P(\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n})$ partitions JK in the ratio, $m:n$.

The y-coordinate of P is

$y=\frac{ny_1+my_2}{m+n}=\frac{7*1+3*5}{3+7}=\frac{11}{5}$